Clustering and Dimensionality Reduction.ipynb

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    "# Clustering and Dimensionality Reduction\n",
    "In the last class, we described the basics of feature engineering--the process of choosing a numerical representation for your data. The techniques that we chose were mostly about defining meaningful correlation relationships between variables. Next, we will explore two other types of multi-variable relationships: low dimensional and clustering. "
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    "## Dimensionality Reduction\n",
    "How do we summarize a very wide set of observations into a small number of key factors? Principal component analysis (PCA) is a statistical procedure to convert a set of observations of correlated variables into a set of values of linearly uncorrelated variables called principal components. This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components. The resulting vectors (each being a linear combination of the variables and containing n observations) are an uncorrelated orthogonal basis set. \n",
    "\n",
    "Let's work with an example dataset to make this a bit more clear. We have a dataset of world flag descriptions."
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       "                bars  stripes  colours  red  green  blue  gold  white  black  \\\n",
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       "name                                                     \n",
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   ],
   "source": [
    "import pandas as pd\n",
    "flag = pd.read_csv('flag.csv',index_col='name')\n",
    "flag"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataset lists out all of the countries of the world and different properties about their national flags. For example, we can find all of the flags that have crescents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Andorra</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Western-Samoa</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yugoslavia</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zaire</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zambia</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zimbabwe</th>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>153 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                bars  stripes  colours  red  green  blue  gold  white  black  \\\n",
       "name                                                                           \n",
       "Afghanistan        0        3        5    1      1     0     1      1      1   \n",
       "Albania            0        0        3    1      0     0     1      0      1   \n",
       "Algeria            2        0        3    1      1     0     0      1      0   \n",
       "American-Samoa     0        0        5    1      0     1     1      1      0   \n",
       "Andorra            3        0        3    1      0     1     1      0      0   \n",
       "...              ...      ...      ...  ...    ...   ...   ...    ...    ...   \n",
       "Western-Samoa      0        0        3    1      0     1     0      1      0   \n",
       "Yugoslavia         0        3        4    1      0     1     1      1      0   \n",
       "Zaire              0        0        4    1      1     0     1      0      0   \n",
       "Zambia             3        0        4    1      1     0     0      0      1   \n",
       "Zimbabwe           0        7        5    1      1     0     1      1      1   \n",
       "\n",
       "                orange  ... circles  crosses  saltires  quarters  sunstars  \\\n",
       "name                    ...                                                  \n",
       "Afghanistan          0  ...       0        0         0         0         1   \n",
       "Albania              0  ...       0        0         0         0         1   \n",
       "Algeria              0  ...       0        0         0         0         1   \n",
       "American-Samoa       1  ...       0        0         0         0         0   \n",
       "Andorra              0  ...       0        0         0         0         0   \n",
       "...                ...  ...     ...      ...       ...       ...       ...   \n",
       "Western-Samoa        0  ...       0        0         0         1         5   \n",
       "Yugoslavia           0  ...       0        0         0         0         1   \n",
       "Zaire                1  ...       1        0         0         0         0   \n",
       "Zambia               1  ...       0        0         0         0         0   \n",
       "Zimbabwe             0  ...       0        0         0         0         1   \n",
       "\n",
       "                crescent  triangle  icon  animate  text  \n",
       "name                                                     \n",
       "Afghanistan            0         0     1        0     0  \n",
       "Albania                0         0     0        1     0  \n",
       "Algeria                1         0     0        0     0  \n",
       "American-Samoa         0         1     1        1     0  \n",
       "Andorra                0         0     0        0     0  \n",
       "...                  ...       ...   ...      ...   ...  \n",
       "Western-Samoa          0         0     0        0     0  \n",
       "Yugoslavia             0         0     0        0     0  \n",
       "Zaire                  0         0     1        1     0  \n",
       "Zambia                 0         0     0        1     0  \n",
       "Zimbabwe               0         1     1        1     0  \n",
       "\n",
       "[153 rows x 21 columns]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flag[flag['red'] > 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or all of the flags that have both green and black:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "        text-align: right;\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bars</th>\n",
       "      <th>stripes</th>\n",
       "      <th>colours</th>\n",
       "      <th>red</th>\n",
       "      <th>green</th>\n",
       "      <th>blue</th>\n",
       "      <th>gold</th>\n",
       "      <th>white</th>\n",
       "      <th>black</th>\n",
       "      <th>orange</th>\n",
       "      <th>...</th>\n",
       "      <th>circles</th>\n",
       "      <th>crosses</th>\n",
       "      <th>saltires</th>\n",
       "      <th>quarters</th>\n",
       "      <th>sunstars</th>\n",
       "      <th>crescent</th>\n",
       "      <th>triangle</th>\n",
       "      <th>icon</th>\n",
       "      <th>animate</th>\n",
       "      <th>text</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Afghanistan</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Belize</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bermuda</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cape-Verde-Islands</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dominica</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ghana</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Guinea-Bissau</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Guyana</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iraq</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Jamaica</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Jordan</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kenya</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kuwait</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Malawi</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Montserrat</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mozambique</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North-Yemen</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Parguay</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rwanda</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sao-Tome</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>St-Kitts-Nevis</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sudan</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Syria</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tanzania</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UAE</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vanuatu</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Venezuela</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zambia</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zimbabwe</th>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>29 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                    bars  stripes  colours  red  green  blue  gold  white  \\\n",
       "name                                                                        \n",
       "Afghanistan            0        3        5    1      1     0     1      1   \n",
       "Belize                 0        2        8    1      1     1     1      1   \n",
       "Bermuda                0        0        6    1      1     1     1      1   \n",
       "Cape-Verde-Islands     1        2        5    1      1     0     1      0   \n",
       "Dominica               0        0        6    1      1     1     1      1   \n",
       "Ghana                  0        3        4    1      1     0     1      0   \n",
       "Guinea-Bissau          1        2        4    1      1     0     1      0   \n",
       "Guyana                 0        0        5    1      1     0     1      1   \n",
       "Iraq                   0        3        4    1      1     0     0      1   \n",
       "Jamaica                0        0        3    0      1     0     1      0   \n",
       "Jordan                 0        3        4    1      1     0     0      1   \n",
       "Kenya                  0        5        4    1      1     0     0      1   \n",
       "Kuwait                 0        3        4    1      1     0     0      1   \n",
       "Malawi                 0        3        3    1      1     0     0      0   \n",
       "Montserrat             0        0        7    1      1     1     1      1   \n",
       "Mozambique             0        5        5    1      1     0     1      1   \n",
       "North-Yemen            0        3        4    1      1     0     0      1   \n",
       "Parguay                0        3        6    1      1     1     1      1   \n",
       "Rwanda                 3        0        4    1      1     0     1      0   \n",
       "Sao-Tome               0        3        4    1      1     0     1      0   \n",
       "St-Kitts-Nevis         0        0        5    1      1     0     1      1   \n",
       "Sudan                  0        3        4    1      1     0     0      1   \n",
       "Syria                  0        3        4    1      1     0     0      1   \n",
       "Tanzania               0        0        4    0      1     1     1      0   \n",
       "UAE                    1        3        4    1      1     0     0      1   \n",
       "Vanuatu                0        0        4    1      1     0     1      0   \n",
       "Venezuela              0        3        7    1      1     1     1      1   \n",
       "Zambia                 3        0        4    1      1     0     0      0   \n",
       "Zimbabwe               0        7        5    1      1     0     1      1   \n",
       "\n",
       "                    black  orange  ... circles  crosses  saltires  quarters  \\\n",
       "name                               ...                                        \n",
       "Afghanistan             1       0  ...       0        0         0         0   \n",
       "Belize                  1       1  ...       1        0         0         0   \n",
       "Bermuda                 1       0  ...       1        1         1         1   \n",
       "Cape-Verde-Islands      1       1  ...       0        0         0         0   \n",
       "Dominica                1       0  ...       1        0         0         0   \n",
       "Ghana                   1       0  ...       0        0         0         0   \n",
       "Guinea-Bissau           1       0  ...       0        0         0         0   \n",
       "Guyana                  1       0  ...       0        0         0         0   \n",
       "Iraq                    1       0  ...       0        0         0         0   \n",
       "Jamaica                 1       0  ...       0        0         1         0   \n",
       "Jordan                  1       0  ...       0        0         0         0   \n",
       "Kenya                   1       0  ...       1        0         0         0   \n",
       "Kuwait                  1       0  ...       0        0         0         0   \n",
       "Malawi                  1       0  ...       0        0         0         0   \n",
       "Montserrat              1       0  ...       0        2         1         1   \n",
       "Mozambique              1       0  ...       0        0         0         0   \n",
       "North-Yemen             1       0  ...       0        0         0         0   \n",
       "Parguay                 1       0  ...       1        0         0         0   \n",
       "Rwanda                  1       0  ...       0        0         0         0   \n",
       "Sao-Tome                1       0  ...       0        0         0         0   \n",
       "St-Kitts-Nevis          1       0  ...       0        0         0         0   \n",
       "Sudan                   1       0  ...       0        0         0         0   \n",
       "Syria                   1       0  ...       0        0         0         0   \n",
       "Tanzania                1       0  ...       0        0         0         0   \n",
       "UAE                     1       0  ...       0        0         0         0   \n",
       "Vanuatu                 1       0  ...       0        0         0         0   \n",
       "Venezuela               1       1  ...       0        0         0         0   \n",
       "Zambia                  1       1  ...       0        0         0         0   \n",
       "Zimbabwe                1       0  ...       0        0         0         0   \n",
       "\n",
       "                    sunstars  crescent  triangle  icon  animate  text  \n",
       "name                                                                   \n",
       "Afghanistan                1         0         0     1        0     0  \n",
       "Belize                     0         0         0     1        1     1  \n",
       "Bermuda                    0         0         0     1        1     0  \n",
       "Cape-Verde-Islands         1         0         0     0        1     0  \n",
       "Dominica                  10         0         0     0        1     0  \n",
       "Ghana                      1         0         0     0        0     0  \n",
       "Guinea-Bissau              1         0         0     0        0     0  \n",
       "Guyana                     0         0         1     0        0     0  \n",
       "Iraq                       3         0         0     0        0     0  \n",
       "Jamaica                    0         0         1     0        0     0  \n",
       "Jordan                     1         0         1     0        0     0  \n",
       "Kenya                      0         0         0     1        0     0  \n",
       "Kuwait                     0         0         0     0        0     0  \n",
       "Malawi                     1         0         0     0        0     0  \n",
       "Montserrat                 0         0         0     1        1     0  \n",
       "Mozambique                 1         0         1     1        0     0  \n",
       "North-Yemen                1         0         0     0        0     0  \n",
       "Parguay                    1         0         0     1        1     1  \n",
       "Rwanda                     0         0         0     0        0     1  \n",
       "Sao-Tome                   2         0         1     0        0     0  \n",
       "St-Kitts-Nevis             2         0         1     0        0     0  \n",
       "Sudan                      0         0         1     0        0     0  \n",
       "Syria                      2         0         0     0        0     0  \n",
       "Tanzania                   0         0         1     0        0     0  \n",
       "UAE                        0         0         0     0        0     0  \n",
       "Vanuatu                    0         0         1     0        1     0  \n",
       "Venezuela                  7         0         0     1        1     0  \n",
       "Zambia                     0         0         0     0        1     0  \n",
       "Zimbabwe                   1         0         1     1        1     0  \n",
       "\n",
       "[29 rows x 21 columns]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flag[ (flag['green'] == 1) & (flag['black'] == 1)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is one variable that we will have clean up before we proceed further. That describes the primary color of the flag."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name\n",
      "Afghanistan       green\n",
      "Albania             red\n",
      "Algeria           green\n",
      "American-Samoa     blue\n",
      "Andorra            gold\n",
      "Name: mainhue, dtype: object\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bars</th>\n",
       "      <th>stripes</th>\n",
       "      <th>colours</th>\n",
       "      <th>red</th>\n",
       "      <th>green</th>\n",
       "      <th>blue</th>\n",
       "      <th>gold</th>\n",
       "      <th>white</th>\n",
       "      <th>black</th>\n",
       "      <th>orange</th>\n",
       "      <th>...</th>\n",
       "      <th>animate</th>\n",
       "      <th>text</th>\n",
       "      <th>mainhue_green</th>\n",
       "      <th>mainhue_red</th>\n",
       "      <th>mainhue_blue</th>\n",
       "      <th>mainhue_gold</th>\n",
       "      <th>mainhue_white</th>\n",
       "      <th>mainhue_orange</th>\n",
       "      <th>mainhue_black</th>\n",
       "      <th>mainhue_brown</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Afghanistan</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Albania</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Algeria</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>American-Samoa</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Andorra</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 28 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                bars  stripes  colours  red  green  blue  gold  white  black  \\\n",
       "name                                                                           \n",
       "Afghanistan        0        3        5    1      1     0     1      1      1   \n",
       "Albania            0        0        3    1      0     0     1      0      1   \n",
       "Algeria            2        0        3    1      1     0     0      1      0   \n",
       "American-Samoa     0        0        5    1      0     1     1      1      0   \n",
       "Andorra            3        0        3    1      0     1     1      0      0   \n",
       "\n",
       "                orange  ...  animate  text  mainhue_green  mainhue_red  \\\n",
       "name                    ...                                              \n",
       "Afghanistan          0  ...        0     0              1            0   \n",
       "Albania              0  ...        1     0              0            1   \n",
       "Algeria              0  ...        0     0              1            0   \n",
       "American-Samoa       1  ...        1     0              0            0   \n",
       "Andorra              0  ...        0     0              0            0   \n",
       "\n",
       "                mainhue_blue  mainhue_gold  mainhue_white  mainhue_orange  \\\n",
       "name                                                                        \n",
       "Afghanistan                0             0              0               0   \n",
       "Albania                    0             0              0               0   \n",
       "Algeria                    0             0              0               0   \n",
       "American-Samoa             1             0              0               0   \n",
       "Andorra                    0             1              0               0   \n",
       "\n",
       "                mainhue_black  mainhue_brown  \n",
       "name                                          \n",
       "Afghanistan                 0              0  \n",
       "Albania                     0              0  \n",
       "Algeria                     0              0  \n",
       "American-Samoa              0              0  \n",
       "Andorra                     0              0  \n",
       "\n",
       "[5 rows x 28 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(flag['mainhue'][:5])\n",
    "\n",
    "#Add a 1-hot encoded column that represents each main hue\n",
    "for hue in flag['mainhue'].unique():\n",
    "    flag['mainhue_'+hue]  = 1*(flag['mainhue'] == hue)\n",
    "\n",
    "flag = flag.drop(columns=['mainhue'])\n",
    "flag[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset has a lot of variables and a relatively few number of observations. Are all the variables equally informative? \n",
    "\n",
    "To answer this question, let's think about what informative means. Which of the following columns is more interesting to a data scientist: a column of all 1's or a column that varies a lot. \n",
    "\n",
    "Convince yourself that we want columns that vary a lot--ones that \"explain\" differences between the observed data. Suppose, we calculate the standard deviation of each attribute to measure this variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bars              1.038339\n",
       "stripes           2.328005\n",
       "colours           1.300154\n",
       "red               0.409315\n",
       "green             0.500334\n",
       "blue              0.501187\n",
       "gold              0.500334\n",
       "white             0.432631\n",
       "black             0.444085\n",
       "orange            0.341556\n",
       "circles           0.463075\n",
       "crosses           0.385387\n",
       "saltires          0.290879\n",
       "quarters          0.435860\n",
       "sunstars          4.396186\n",
       "crescent          0.231869\n",
       "triangle          0.347025\n",
       "icon              0.435615\n",
       "animate           0.401808\n",
       "text              0.275798\n",
       "mainhue_green     0.367363\n",
       "mainhue_red       0.482950\n",
       "mainhue_blue      0.405612\n",
       "mainhue_gold      0.298000\n",
       "mainhue_white     0.317904\n",
       "mainhue_orange    0.142471\n",
       "mainhue_black     0.158868\n",
       "mainhue_brown     0.101271\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flag.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is this accurate? Why might \"stars\" be the highest variance column? \n",
    "\n",
    "Making variance comparisons between columns that have different scaling properties is faulty. So we always have to \"normalize\" our data, when doing such kind of analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sunstars          0.087924\n",
       "mainhue_brown     0.101271\n",
       "quarters          0.108965\n",
       "circles           0.115769\n",
       "mainhue_orange    0.142471\n",
       "mainhue_black     0.158868\n",
       "stripes           0.166286\n",
       "colours           0.185736\n",
       "crosses           0.192693\n",
       "bars              0.207668\n",
       "crescent          0.231869\n",
       "text              0.275798\n",
       "saltires          0.290879\n",
       "mainhue_gold      0.298000\n",
       "mainhue_white     0.317904\n",
       "orange            0.341556\n",
       "triangle          0.347025\n",
       "mainhue_green     0.367363\n",
       "animate           0.401808\n",
       "mainhue_blue      0.405612\n",
       "red               0.409315\n",
       "white             0.432631\n",
       "icon              0.435615\n",
       "black             0.444085\n",
       "mainhue_red       0.482950\n",
       "gold              0.500334\n",
       "green             0.500334\n",
       "blue              0.501187\n",
       "dtype: float64"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#scale all variables to be between 0 and 1\n",
    "#iterate through all columns\n",
    "for c in flag.columns:\n",
    "    flag[c] = (flag[c]-flag[c].min())/(flag[c].max() - flag[c].min())\n",
    "    #we know the min val for all is 0\n",
    "\n",
    "flag.std().sort_values()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This analysis tells us which single columns are the most informative but what about combinations of columns? Two columns can be exactly correlated to each other but vary a lot individually. This leads to the idea of Principal Component Analysis. The precise math is beyond the scope of this class (better for a machine learning class) but the basic intuition is that the algorithm searches for weighted averages of columns that have the highest variance. One it finds the best one, it finds the next best weighted average subject to that combination being uncorrelated with the first, and so on and so forth. \n",
    "\n",
    "To apply PCA, we will use the scikit-learn package. The first thing that we will have to do is to convert the data into a numpy array (array of numbers)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.21428571, 0.57142857, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.        , 0.        , 0.28571429, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.4       , 0.        , 0.28571429, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       ...,\n",
       "       [0.        , 0.        , 0.42857143, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.6       , 0.        , 0.42857143, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.        , 0.5       , 0.57142857, ..., 0.        , 0.        ,\n",
       "        0.        ]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = flag.to_numpy()\n",
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we use the PCA module for the scikit-learn package to fit a PCA model to the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2) #find 2 principal components\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This process outputs a few different things. First, it computes two weighted averages of columns called the principal components--you can think of these as the \"axes\" over which the data varies the most:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Principal Component 1: \n",
      " (Negative) [(-0.2659816028533505, 'white'), (-0.25452500904979364, 'blue'), (-0.12941798418053677, 'mainhue_white'), (-0.11252535114809306, 'mainhue_blue'), (-0.04528345460086802, 'mainhue_red')] \n",
      "\n",
      " (Positive) [(0.2867829693680826, 'icon'), (0.29186803466547395, 'black'), (0.301800611052263, 'animate'), (0.4487057346308544, 'green'), (0.4967532787453514, 'gold')]\n",
      "\n",
      "\n",
      "Principal Component 2: \n",
      " (Negative) [(-0.32844892829767997, 'mainhue_red'), (-0.15207728098211426, 'red'), (-0.09375885566128271, 'black'), (-0.08865119493564189, 'mainhue_green'), (-0.054591826848101876, 'green')] \n",
      "\n",
      " (Positive) [(0.21398865775168574, 'orange'), (0.23418896594610347, 'animate'), (0.2884050701959082, 'icon'), (0.4317407484665297, 'mainhue_blue'), (0.5414664420892669, 'blue')]\n"
     ]
    }
   ],
   "source": [
    "pc1, pc2 = pca.components_\n",
    "\n",
    "weights1 = list(zip(pc1, flag.columns))\n",
    "weights1.sort()\n",
    "\n",
    "print('Principal Component 1: \\n (Negative)',weights1[:5], '\\n\\n (Positive)' ,weights1[-5:])\n",
    "\n",
    "print()\n",
    "print()\n",
    "\n",
    "weights2 = list(zip(pc2, flag.columns))\n",
    "weights2.sort()\n",
    "\n",
    "print('Principal Component 2: \\n (Negative)',weights2[:5], '\\n\\n (Positive)' ,weights2[-5:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, the model also returns an explained variance (how much of the variance these two components explain) 100% is the maximum. Given that there are 30 variables, it is quite significant that only 2 variables explain more than 30% of all the variation in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.17299924 0.15548248]\n"
     ]
    }
   ],
   "source": [
    "print(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, you can use this to perform a dimensionality reduction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline  \n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "Y = pca.transform(X)\n",
    "plt.scatter(Y[:,0], Y[:,1])\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to interpret this figure a bit more. Let's see where all the \"Baathist\" Arab countries lie on this plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "arab = ['Syria', 'Jordan', 'Kuwait', 'UAE']\n",
    "arab_index = [list(flag.index.values).index(a) for a in arab]\n",
    "plt.scatter(Y[:,0], Y[:,1])\n",
    "plt.scatter(Y[arab_index,0], Y[arab_index,1],color='r')\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or we can look at all of the countries in northern europe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ne = ['Norway', 'Denmark', 'Finland', 'Iceland']\n",
    "ne_index = [list(flag.index.values).index(a) for a in ne]\n",
    "plt.scatter(Y[:,0], Y[:,1])\n",
    "plt.scatter(Y[ne_index,0], Y[ne_index,1],color='r')\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering\n",
    "When we were playing around with the data we manually used data clusters that we roughly knew about to validate our model. How do we do this automatically? Clustering is the task of dividing the population or data points into a number of groups such that data points in the same groups are more similar to other data points in the same group than those in other groups. In particular, we will focus on a simple form of clustering called \"k-means\". k-means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. \n",
    "\n",
    "Again, the mathematical details are better left for a machine learning class but you can see how to use scikit-learn to do this. \n",
    "\n",
    "Suppose, we have a dataset of credit card customers and we want to break them into customer segments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>BALANCE</th>\n",
       "      <th>BALANCE_FREQUENCY</th>\n",
       "      <th>PURCHASES</th>\n",
       "      <th>ONEOFF_PURCHASES</th>\n",
       "      <th>INSTALLMENTS_PURCHASES</th>\n",
       "      <th>CASH_ADVANCE</th>\n",
       "      <th>PURCHASES_FREQUENCY</th>\n",
       "      <th>ONEOFF_PURCHASES_FREQUENCY</th>\n",
       "      <th>PURCHASES_INSTALLMENTS_FREQUENCY</th>\n",
       "      <th>CASH_ADVANCE_FREQUENCY</th>\n",
       "      <th>CASH_ADVANCE_TRX</th>\n",
       "      <th>PURCHASES_TRX</th>\n",
       "      <th>CREDIT_LIMIT</th>\n",
       "      <th>PAYMENTS</th>\n",
       "      <th>MINIMUM_PAYMENTS</th>\n",
       "      <th>PRC_FULL_PAYMENT</th>\n",
       "      <th>TENURE</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CUST_ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C10001</th>\n",
       "      <td>40.900749</td>\n",
       "      <td>0.818182</td>\n",
       "      <td>95.40</td>\n",
       "      <td>0.00</td>\n",
       "      <td>95.40</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.166667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.083333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>201.802084</td>\n",
       "      <td>139.509787</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>12</td>\n",
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       "    <tr>\n",
       "      <th>C10002</th>\n",
       "      <td>3202.467416</td>\n",
       "      <td>0.909091</td>\n",
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       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6442.945483</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>7000.0</td>\n",
       "      <td>4103.032597</td>\n",
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       "      <td>7500.0</td>\n",
       "      <td>0.000000</td>\n",
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       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>C10005</th>\n",
       "      <td>817.714335</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>16.00</td>\n",
       "      <td>16.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.083333</td>\n",
       "      <td>0.083333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>678.334763</td>\n",
       "      <td>244.791237</td>\n",
       "      <td>0.000000</td>\n",
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       "      <th>C19186</th>\n",
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       "      <td>291.12</td>\n",
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       "      <td>291.12</td>\n",
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       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>325.594462</td>\n",
       "      <td>48.886365</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>6</td>\n",
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       "    <tr>\n",
       "      <th>C19187</th>\n",
       "      <td>19.183215</td>\n",
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       "      <td>300.00</td>\n",
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       "      <td>300.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.833333</td>\n",
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       "      <td>0</td>\n",
       "      <td>6</td>\n",
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       "      <td>275.861322</td>\n",
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       "      <th>C19188</th>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>81.270775</td>\n",
       "      <td>82.418369</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>6</td>\n",
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       "    <tr>\n",
       "      <th>C19189</th>\n",
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       "      <td>0.00</td>\n",
       "      <td>36.558778</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.166667</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>500.0</td>\n",
       "      <td>52.549959</td>\n",
       "      <td>55.755628</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>6</td>\n",
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       "    <tr>\n",
       "      <th>C19190</th>\n",
       "      <td>372.708075</td>\n",
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       "      <td>1093.25</td>\n",
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       "      <td>127.040008</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.666667</td>\n",
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       "      <td>0.333333</td>\n",
       "      <td>2</td>\n",
       "      <td>23</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>63.165404</td>\n",
       "      <td>88.288956</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>8950 rows × 17 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             BALANCE  BALANCE_FREQUENCY  PURCHASES  ONEOFF_PURCHASES  \\\n",
       "CUST_ID                                                                \n",
       "C10001     40.900749           0.818182      95.40              0.00   \n",
       "C10002   3202.467416           0.909091       0.00              0.00   \n",
       "C10003   2495.148862           1.000000     773.17            773.17   \n",
       "C10004   1666.670542           0.636364    1499.00           1499.00   \n",
       "C10005    817.714335           1.000000      16.00             16.00   \n",
       "...              ...                ...        ...               ...   \n",
       "C19186     28.493517           1.000000     291.12              0.00   \n",
       "C19187     19.183215           1.000000     300.00              0.00   \n",
       "C19188     23.398673           0.833333     144.40              0.00   \n",
       "C19189     13.457564           0.833333       0.00              0.00   \n",
       "C19190    372.708075           0.666667    1093.25           1093.25   \n",
       "\n",
       "         INSTALLMENTS_PURCHASES  CASH_ADVANCE  PURCHASES_FREQUENCY  \\\n",
       "CUST_ID                                                              \n",
       "C10001                    95.40      0.000000             0.166667   \n",
       "C10002                     0.00   6442.945483             0.000000   \n",
       "C10003                     0.00      0.000000             1.000000   \n",
       "C10004                     0.00    205.788017             0.083333   \n",
       "C10005                     0.00      0.000000             0.083333   \n",
       "...                         ...           ...                  ...   \n",
       "C19186                   291.12      0.000000             1.000000   \n",
       "C19187                   300.00      0.000000             1.000000   \n",
       "C19188                   144.40      0.000000             0.833333   \n",
       "C19189                     0.00     36.558778             0.000000   \n",
       "C19190                     0.00    127.040008             0.666667   \n",
       "\n",
       "         ONEOFF_PURCHASES_FREQUENCY  PURCHASES_INSTALLMENTS_FREQUENCY  \\\n",
       "CUST_ID                                                                 \n",
       "C10001                     0.000000                          0.083333   \n",
       "C10002                     0.000000                          0.000000   \n",
       "C10003                     1.000000                          0.000000   \n",
       "C10004                     0.083333                          0.000000   \n",
       "C10005                     0.083333                          0.000000   \n",
       "...                             ...                               ...   \n",
       "C19186                     0.000000                          0.833333   \n",
       "C19187                     0.000000                          0.833333   \n",
       "C19188                     0.000000                          0.666667   \n",
       "C19189                     0.000000                          0.000000   \n",
       "C19190                     0.666667                          0.000000   \n",
       "\n",
       "         CASH_ADVANCE_FREQUENCY  CASH_ADVANCE_TRX  PURCHASES_TRX  \\\n",
       "CUST_ID                                                            \n",
       "C10001                 0.000000                 0              2   \n",
       "C10002                 0.250000                 4              0   \n",
       "C10003                 0.000000                 0             12   \n",
       "C10004                 0.083333                 1              1   \n",
       "C10005                 0.000000                 0              1   \n",
       "...                         ...               ...            ...   \n",
       "C19186                 0.000000                 0              6   \n",
       "C19187                 0.000000                 0              6   \n",
       "C19188                 0.000000                 0              5   \n",
       "C19189                 0.166667                 2              0   \n",
       "C19190                 0.333333                 2             23   \n",
       "\n",
       "         CREDIT_LIMIT     PAYMENTS  MINIMUM_PAYMENTS  PRC_FULL_PAYMENT  TENURE  \n",
       "CUST_ID                                                                         \n",
       "C10001         1000.0   201.802084        139.509787          0.000000      12  \n",
       "C10002         7000.0  4103.032597       1072.340217          0.222222      12  \n",
       "C10003         7500.0   622.066742        627.284787          0.000000      12  \n",
       "C10004         7500.0     0.000000               NaN          0.000000      12  \n",
       "C10005         1200.0   678.334763        244.791237          0.000000      12  \n",
       "...               ...          ...               ...               ...     ...  \n",
       "C19186         1000.0   325.594462         48.886365          0.500000       6  \n",
       "C19187         1000.0   275.861322               NaN          0.000000       6  \n",
       "C19188         1000.0    81.270775         82.418369          0.250000       6  \n",
       "C19189          500.0    52.549959         55.755628          0.250000       6  \n",
       "C19190         1200.0    63.165404         88.288956          0.000000       6  \n",
       "\n",
       "[8950 rows x 17 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "customers = pd.read_csv('cc.csv', index_col='CUST_ID')\n",
    "customers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's clean up this data a bit. There are a few NaN numbers that we should remove from the dataset. There are a handful of customers that have not made any payments yet and we should set their minimum payments to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "customers = customers.fillna(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>BALANCE</th>\n",
       "      <th>BALANCE_FREQUENCY</th>\n",
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       "      <th>TENURE</th>\n",
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       "      <td>291.12</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>325.594462</td>\n",
       "      <td>48.886365</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C19187</th>\n",
       "      <td>19.183215</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>300.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>300.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>275.861322</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C19188</th>\n",
       "      <td>23.398673</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>144.40</td>\n",
       "      <td>0.00</td>\n",
       "      <td>144.40</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>81.270775</td>\n",
       "      <td>82.418369</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C19189</th>\n",
       "      <td>13.457564</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>36.558778</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.166667</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>500.0</td>\n",
       "      <td>52.549959</td>\n",
       "      <td>55.755628</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C19190</th>\n",
       "      <td>372.708075</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>1093.25</td>\n",
       "      <td>1093.25</td>\n",
       "      <td>0.00</td>\n",
       "      <td>127.040008</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>2</td>\n",
       "      <td>23</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>63.165404</td>\n",
       "      <td>88.288956</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8950 rows × 17 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             BALANCE  BALANCE_FREQUENCY  PURCHASES  ONEOFF_PURCHASES  \\\n",
       "CUST_ID                                                                \n",
       "C10001     40.900749           0.818182      95.40              0.00   \n",
       "C10002   3202.467416           0.909091       0.00              0.00   \n",
       "C10003   2495.148862           1.000000     773.17            773.17   \n",
       "C10004   1666.670542           0.636364    1499.00           1499.00   \n",
       "C10005    817.714335           1.000000      16.00             16.00   \n",
       "...              ...                ...        ...               ...   \n",
       "C19186     28.493517           1.000000     291.12              0.00   \n",
       "C19187     19.183215           1.000000     300.00              0.00   \n",
       "C19188     23.398673           0.833333     144.40              0.00   \n",
       "C19189     13.457564           0.833333       0.00              0.00   \n",
       "C19190    372.708075           0.666667    1093.25           1093.25   \n",
       "\n",
       "         INSTALLMENTS_PURCHASES  CASH_ADVANCE  PURCHASES_FREQUENCY  \\\n",
       "CUST_ID                                                              \n",
       "C10001                    95.40      0.000000             0.166667   \n",
       "C10002                     0.00   6442.945483             0.000000   \n",
       "C10003                     0.00      0.000000             1.000000   \n",
       "C10004                     0.00    205.788017             0.083333   \n",
       "C10005                     0.00      0.000000             0.083333   \n",
       "...                         ...           ...                  ...   \n",
       "C19186                   291.12      0.000000             1.000000   \n",
       "C19187                   300.00      0.000000             1.000000   \n",
       "C19188                   144.40      0.000000             0.833333   \n",
       "C19189                     0.00     36.558778             0.000000   \n",
       "C19190                     0.00    127.040008             0.666667   \n",
       "\n",
       "         ONEOFF_PURCHASES_FREQUENCY  PURCHASES_INSTALLMENTS_FREQUENCY  \\\n",
       "CUST_ID                                                                 \n",
       "C10001                     0.000000                          0.083333   \n",
       "C10002                     0.000000                          0.000000   \n",
       "C10003                     1.000000                          0.000000   \n",
       "C10004                     0.083333                          0.000000   \n",
       "C10005                     0.083333                          0.000000   \n",
       "...                             ...                               ...   \n",
       "C19186                     0.000000                          0.833333   \n",
       "C19187                     0.000000                          0.833333   \n",
       "C19188                     0.000000                          0.666667   \n",
       "C19189                     0.000000                          0.000000   \n",
       "C19190                     0.666667                          0.000000   \n",
       "\n",
       "         CASH_ADVANCE_FREQUENCY  CASH_ADVANCE_TRX  PURCHASES_TRX  \\\n",
       "CUST_ID                                                            \n",
       "C10001                 0.000000                 0              2   \n",
       "C10002                 0.250000                 4              0   \n",
       "C10003                 0.000000                 0             12   \n",
       "C10004                 0.083333                 1              1   \n",
       "C10005                 0.000000                 0              1   \n",
       "...                         ...               ...            ...   \n",
       "C19186                 0.000000                 0              6   \n",
       "C19187                 0.000000                 0              6   \n",
       "C19188                 0.000000                 0              5   \n",
       "C19189                 0.166667                 2              0   \n",
       "C19190                 0.333333                 2             23   \n",
       "\n",
       "         CREDIT_LIMIT     PAYMENTS  MINIMUM_PAYMENTS  PRC_FULL_PAYMENT  TENURE  \n",
       "CUST_ID                                                                         \n",
       "C10001         1000.0   201.802084        139.509787          0.000000      12  \n",
       "C10002         7000.0  4103.032597       1072.340217          0.222222      12  \n",
       "C10003         7500.0   622.066742        627.284787          0.000000      12  \n",
       "C10004         7500.0     0.000000          0.000000          0.000000      12  \n",
       "C10005         1200.0   678.334763        244.791237          0.000000      12  \n",
       "...               ...          ...               ...               ...     ...  \n",
       "C19186         1000.0   325.594462         48.886365          0.500000       6  \n",
       "C19187         1000.0   275.861322          0.000000          0.000000       6  \n",
       "C19188         1000.0    81.270775         82.418369          0.250000       6  \n",
       "C19189          500.0    52.549959         55.755628          0.250000       6  \n",
       "C19190         1200.0    63.165404         88.288956          0.000000       6  \n",
       "\n",
       "[8950 rows x 17 columns]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "customers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, lets featurize this data and visualize what we are working with. PCA is actually a great way to summarize very high dimensional data into a 2-d plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = customers.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XiIg0gUp3Mn9GQbOYu79mZkt4M+tLRESkqEpB5tdE07p0F5SfCmxJpEbSFLI4XYyI1F+l5rLrgVeLlL8a9okMk5Wp8kUkfZXuZI519x2Fhe6+I0xqKTLMWKduL3cX1Mx3SM383mT8qhRk2srs07BsGaazq6foKH6obrqYcpNmQvOuW5/mZKEKbpKkSs1lW83s04WFZvYnwLZkqiSNKn+hLGWCWcXldcvdBWV1Qs1aSOu9qWlTklbpTuZy4C4zu4Q3g0oHcATwkSQrJo2n2IUybiBMYVTuW/poJs3MwoSaoxG/gyg16Czp95aVVUCleZW9k3H3l9z9vwJXA3vCz9Xufrq7/zL56kkjGckFsdS39FKTYx7f1lp2X6MpvIMoJen3luWZsKU5lL2TMbMjgT8FTgB2ADe5+6F6VEwaT6lZlUvJX8ji3+iPas2RazH6B9689MYXsGqWxa0q3fVBfd6bZsKWpFXqk1lH1Dy2Azgb+F+J10gaVrH15ss5vq112Df63r5++gecCWEIcHzSzNFOqNnZ1cOiNZsr9gfVU7k7hXpOFlrs36xRA7dkU6U+mZPc/WQAM7sJeCT5Kkmjiq83X80dzYrFc0p+oz/sb17sCte0H8mFt5qsrTSyq0rdQbS3tfLQyjMTfe24+L+ZssskCWXXkzGzn7n7KaUeN6NmX0+mXhfUzq4eLt+wveT+ttYc2686i1kr7y3bJzHWi+6iNZvLXsw7u3pY8b3H6D/8Zi1yE4y1H39/ohdaraUjzWZU68kA7w9LGL9qZq8B78tvm1mxmQAkw+qZrrp0fjttrbmi+wxYfV40v2qltv+xdkBX6thevXHnkAAD0H/Y+dyG7Yk2q2ktHRkvyjaXuXv1DeySefVOV1193txh39YNuOS0GYOvt2LxnGHHxI21A7pSx3ZvX3/R5zkkPhhSa+nIeFCpT0aaSKlv9aX6T4o1rUH17ffVtPfnt1dv3Dnsgl+LDuhiQaza82q8SHmaKUCqoSAzjpT6Vm9EF4z4BaJYh/nlG7YzATgcjqlm6pP8t/X8BelzG7azdtMuzjhxKg8+tW/wApVvPqv1RatSoDt6co4DB4vfzUDxNOusX1DrUdc0p8GRxlK24388auaO/86uHj63YXvRjvZ4B3tnVw//87bHBkfoV9JixmH3ohe0zq4erv7+zrIXckiv0/vKzh3csuX5kvvbw3tqlE76eiUUVEqokPFntB3/iTKzb5nZy2b281jZFDO738yeDr+PDuVmZjeYWbeZPW5m8ay3ZeH4p81sWax8gZntCM+5wcyMcWzp/PaK05fkL1LVBhiIposplkiQP1elAANR09TqjTvrOp6ls6uHO7aVfo18s1ojzZlWr7pqpgCpVqpBBvg2sKSgbCXwgLvPBh4IjyEaDDo7/CwHvgFRUAKuAhYSLaZ2VT4whWM+HXte4WuNO+0VpmapZiR6OfEL2kjP1dvXX9eJGsvVL57t1UgX1HrVtZmm+JFkpdon4+7/VmRdmvOB3w3b64CfAF8I5Td71L63xczazOy4cOz97r4fwMzuB5aY2U+At7v7llB+M7AU+EFy7yj7KnWE1+JilD/HWM/V1z/AFbdt53tbn2fL7gMMuNNixsULp/OVpSePue+hVP0MhjT5NNLUK/Wq61gSKmR8SftOpphj3f3FsP1LouWfAdqBF2LH7Q1l5cr3FikfxsyWm9lWM9u6b9++sb+DDKs0PqMWF6P8OWpxrsMODz2zf7D5bsCdW7Y8z+wv3svlG7YPufO5fMN25n/5R1Xf/VT7bbyRpl6pV101zkeqlensMnd3M0s8M8HdbwRuhKjjP+nXS1qlb/jlxmecceLUsh3h1chf0CqNgRmL/sPFyw8c7OdzG7Zz+Ybtg532pd7risVzio72L7wgN9LUK/Wsq8b5SDWyGGReMrPj3P3F0Bz2cijvAabHjpsWynp4s3ktX/6TUD6tyPFNbSSppcWC0YNPje1O7i1HtAymKh/f1spHF7QPpiof1Zrj128cGjLDchLyZ+/p7WPF7Y+xeuNOXunrH3bB3frc/mGj/SmRGtJIF9RGqqs0v9RTmEOfzD3u/t7weC3wK3dfY2YrgSnu/nkzOxe4DDiHqJP/Bnc/NXT8bwPy2WY/Axa4+34zewT4c+Bh4D7g79z9vnL1abQU5sJA8evXD5Ucxd7e1jo4PqWntw+DIdlmrbmWqu862ooEjFyLMTDgxG8y4vOAlUp7rad8Oi9QMp0bqHgXlP+79/T20WLGgHvF54g0s1IpzKkGGTP7LtFdyDuAl4iyxDqB24AZwHPAJ0LAMODviTLEDgKfcvet4Tx/DHwxnPYad/+XUN5BlMHWStTh/z+8whtupCBTbEzEWBUGnlKuv3AeMLRZZv+vX6evVDtWhuQz7CoFvFLjS8r93cuNSRlLokIjDQaV8SmTQSaLGiXIjHTAZK215lr46IJ27n38xarGwWRJvkWsmr9cscGFle7Iij1nLIMkNWOzNIJMDsaU0RnNgMla6+sf4JYtz485wIxkkbO4eFbTW44Y2TnKLeVcqFiac6XU7GL7r/7+zlEPkmykwaAihRRkGtBYB0xmRYsZff0Dg6tgjkS82eiaj5xcMlgVnjufzrti8RxyLZVfuFgwqhSgCvd3dvWUDMbVjCVqpMGgIoUUZDKmmqWCG/3ikr+05+/EChO8YHhwKJQfG5NPV540cULRO5oWM46enCs+lqPCjWCp8SXllpku9pxydxzV3FFpdL00MgWZDKl2UbGJDf6vVk0jX7UNgfnjevv6OfjG8Lu7/sPOgYPD05fXbto1PH2ZKChVGlwYH4iYfw5lnlPuS0E1gyQbaTCoSKEsjpMZt6pZVOyDX/tJyYGIzWQ03U3lnlI4XqjUhb8wFblUVtdIxqKUmuqlrTVX1TkaaTCoSCFllxVIM7ts5sp7U3nd8SSf+VUpQyyfPXfHtp4xZ3VVmx2mNGVpZMouy7jOrp5Sg80laJlg5Cp01lT6G+bvYMr1q0B0B/ndh1+oSVZXNfN8VdtUKtJo1FyWEas37qy6H2K8etukiaw+b+7gSPtiMxbkp7EpdZeS7yyPN0GVOrZUivhoEi8qNa9V01Qq0ogUZFJ2yT/9Ow89sz/tajSE3r5+Lt+wHYj6Mz70/uOGLOEcb14q1UQV7yzPX/hLNZ3lp4splERWl9KUpVkpyKRIAWb0evv6uWXL8/zBaTP4ytKTix5zZG7CYJBpa82x+ry5RftAyt0VFeuTSSKrq5HWrBEZCQWZOrqycwffefj5ouNCZHRu3fI8He+aUrR/Ix4cXj80NCWv8BjnzXnb4tllHe+awqo7Hx+ck+31QwNsfW5/zZuwtAiYNCt1/NfJJf/079yyRQGm1pxoypa4aqZhKXZMPsA8tPLMIcsBxCf9POxwy5bnubJzR03fhxYBk2alFOYCtU5hvrJzx5gXAZPKjp6cozcMuizVkW/AdRfOK9vZb8Cza84dfPyeVfcV7ZdpMeOZa8+pRdVFmoJSmFOgAFOdfNpxe1sr1184j6Mn50Z8jgMH+wdTf0ulMTvRGjLlxsfk+0Dy0/uUyjBLc3JSkUaiIJMgBZjqONGdwS96+1i7aRfnvu+4MZ9vNPvyfSDxMSul5KeSEZHy1PGfgA9+7Sc8/fKv065GQ8nfGfT09rHh0ReYnJvAwTrOnxPv7F+0ZnPFWa4vXji97H4RiSjI1EhnV8/gGA4Zm/4BJzfBRrQc9FgULjJWbmxKixkXL5xeMm1aRIZSc1kNXNm5QwGmxg72H+ajC9oHm6VazFj0nimDMx9X0tZaXb9OsTTho0o8d3JuAu886khu3fJ8yWUYRGQoBZkx6uzqUd9LQu7Y1jPYjDbgzs+ef4UVi+dUNcfbh95/XMXjSqUJl+puOdh/WHOLiYyQmsvGSEvgJqfUWJdyacp5Dz61r2wnf2ETWVxvlUtKZ31uMc3qLFnQ9HcyZrbEzHaZWbeZraz1+TW3VH319PZVnEEZon+XybniH2+j/GJhI5nKJav//prVWbKiqYOMmbUAXwfOBk4CLjazk2r5Gppbqr5azIatTFlMa5nstEtOm1H2G/2KxXMqLimQl9V//2pmPRCph2ZvLjsV6Hb33QBmth44H3iiVi+wYvEcPrdhu6bpr5N8H01+BuVSsy33HSqelWZG0cyweNPSUa05CsPTBKPolEBnnDi1ZLNUms1VmtVZsqLZg0w78ELs8V5gYeFBZrYcWA4wY8aMEb1A/qLx+dsf440BhZqkFd69lFqauFS2X+FA/c6uHq7+/k4OxPphevuG98mUmnPunsdeHDJTc09vH5dv2M4X73yc/gGn//Cb43/iyz8nTbM6S1Y0e5CpirvfCNwI0dxlI31+fEEqLaGcrGJ9KcUWBCt1dxlvBCt2FzRSxQISULSprp6JAprVWbKi2YNMDxAfmj0tlCVmz5pzNTAzQaUu0IVNU0dMnDBsen+AyUe8mTBQrN8iafVqrip1h6fsMqm3Zg8yjwKzzWwWUXC5CPj9pF80/x85vg6JjF2piTML70jKpTcffOPNoDKSC36uxcAZbP6C6M7gyNyEIU1tldSzuarSks8i9dDUQcbdD5nZZcAmoAX4lrvvrPC0moj/B9cKmLXxn785xJWdO4YsuXzGiVP57sMvVD0rcvwiX268TW6C8dYjJw4uH5BvZiq8MwCqbnKrlDot0oy0nkyBWq8nk7fwmvt56bU3an5eqV5rrmXICP9SfTLFlmoup1jyQCl7YmvVSHU0qLQxaD2ZlD38pQ/y9knlBxBKclrM+OiCoc1HxVajvP7CeWy/6qwRXcSWzm+n6y/PqrgOTrXzrsmbNKi08TV1c1nWPH71EjWdpWTAnTu29dDxrinDAk2tvhWXm45GmV2jU25Qqe5mGoPuZOrs1k+fzp4153L9hfMqTo0itZX0iPdSnfotZkUn4pTKNKi08SnIpCTfVDOapYZl9JK8OBWbU60118L//sT7FWBGqVTg1qDSxqEgk6J8W/71F85jYpVzZcnYJHlxKtbHozuYsSkVuNX02DiUXVYgqeyyalzZuUNr09RBuzKUGoqyyxpDqewyBZkCaQaZvHlX/6jkdCVSG4XpzM1AF2NJk1KYG8jq8+YqKWCUchMsGp1fQa2TADq7eli0ZjOzVt6bytLMSvWVrFKQyaBq1kuR4voPO4dKTZlcoFZJAFm4wGv9GMkqjZPJqPj4jXwzSKUlhyVSbQtwrZIAsjCWQ6m+klUKMg2g2IDBWSvvHRcLpbWYVT0v2UjVKkMpCxd4rR8jWaXmsgY1Hi4erbkWLl44PZH+qZYapoxnYSyHUn0lqxRkGtSKxXNo9pE1ff0D3LLleSZNnMDRk3MY0XT/uYIAkX/UYsX/IsXiycBhr1l/RdIX+GqSCjRGR7JKKcwFspDCXK0rO3dw65bnx0WzGUQB5qoPz2Xrc/sHp/dvMePihdP5ytKTi86q3JprKTkNvwHPjmJW5GKpwpDMAmGl3pMCiGSNxslUqZGCDAy94FXzL9maa+GUGUexZfeBxPo6kpSbYGDQPzB08bD8RbdYACiVNNHe1spDK88c0evX+6K/aM3mmtVdJEmlgow6/htcPCmg1AXJDHCKfsMeaZBKW3+R9OR4JlepWZVrtd59vTPJspBUIDIWCjJNZMXiOSP+ll1NkGoE5S66tVzvvt4XfWWNSaNTkGkiY72YFgtSjWKCGbNW3lvyPY923ZjC5re2ybmiK2AmddEv9cVBWWPSKBRkmsxYFuEqFqTOOHEq9z7+YlVLC6cp37+UH20PjLn5qrD/pae3b3DamsI+oaQu+rW8CxNJgzr+CzRax3/SinV051oM3Ok/nF698oM0Sw3WrEXHeKnmw7bWHG+ZNFEXfZGYTE2QaWYfN7OdZnbYzDoK9q0ys24z22Vmi2PlS0JZt5mtjJXPMrOHQ/kGMzsilE8Kj7vD/pn1en/NpFhHd/+A89Yjc2F1z3SGWg2405prKZkhV4s+klLneKWvn4dWnsmza87loZVnKsCIlJHWYMyfAxcA/xYvNLOTgIuAucAS4B/MrMXMWoCvA2cDJwEXh2MBvgpc5+4nAAeAS0P5pcCBUH5dOE5GqNSFNt989uRfnc31F85LZYXPvl/rkzwAAAtQSURBVP6BkgMwa9FHkoWR/CKNLpUg4+5Punux4dbnA+vd/XV3fxboBk4NP93uvtvd3wDWA+ebmQFnAreH568DlsbOtS5s3w58IBwvI1DugpofMR9f4bPeSxQMuA+bASA3wWrSR6KpWkTGLmvTyrQDL8Qe7w1lpcqPAXrd/VBB+ZBzhf2vhOOHMbPlZrbVzLbu27evRm+lOZS7oP6it2/IlCdrN+3ilBlH1X26m2FdQzWqgKZqERm7xLLLzOzHwDuL7PqSu9+d1OuOhrvfCNwIUcd/ytXJlKXz21m9cWfRlTrbJueGZV+lMahzoGCAZv+A12xw5Fiy9UQkwSDj7r83iqf1ANNjj6eFMkqU/wpoM7OJ4W4lfnz+XHvNbCJwVDheRmj1eXOHZZgZ8Jv+AfoKUsxGEmAMuOS0GXS8awpXf39nTdOkq+n413LFIsnLWnPZRuCikBk2C5gNPAI8CswOmWRHECUHbPQo//pB4GPh+cuAu2PnWha2PwZsduVrj8rS+e18dEH7kFYoh2EBZqQcuGNb9J2g6y/PYs+ac9mz5lyuv3DemFu8jmotn4iQhdUsRcaDtFKYP2Jme4HTgXvNbBOAu+8EbgOeAH4IfNbdB8JdymXAJuBJ4LZwLMAXgCvMrJuoz+WmUH4TcEwovwIYTHuWkXvwqX1V36WMJEAUWyJ46fx2LjltxrDz5AdCVlWHCodpuWKR+khlxL+73wXcVWLfNcA1RcrvA+4rUr6bKPussPw3wMfHXFkBqh930ppr4aML2nnwqX1DZg148Kl9JedFK3buryw9mY53TSk6pf7lG7ZXrEdvhaY3TTwpUh+aVkaqUmqixqMn55h8RHWj30uNoC+VJl2q072aIFNpLIsmnhSpj6z1yUhGlRozctWH51Y9+r1W404qDfys5pwaAyNSH7qTkarUYqLGWk32eNWH57Li9seGTFKZ117hnPGMsqNacxyZm0DvwX5ll4kkRBNkFtAEmY1hNOnHWspYJDlaGVOaymgGSdZ7VUsRUZ+MjCPKKBOpPwUZGTc0q7JI/SnIyLihjDKR+lOfjIwbWspYpP4UZGRc0azKIvWl5jIREUmMgoyIiCRGQUZERBKjPhnJFC0kJtJcFGQkMwqnfckvJAYo0Ig0KDWXSWZoITGR5qMgI5mhaV9Emo+CjGSGpn0RaT4KMpIZmvZFpPmo418yQ9O+iDSfVIKMma0FPgy8ATwDfMrde8O+VcClwADw5+6+KZQvAf4WaAH+2d3XhPJZwHrgGGAb8El3f8PMJgE3AwuAXwEXuvueur1JGRVN+yLSXNJqLrsfeK+7vw/4f8AqADM7CbgImAssAf7BzFrMrAX4OnA2cBJwcTgW4KvAde5+AnCAKEARfh8I5deF40REpI5SCTLu/iN3PxQebgGmhe3zgfXu/rq7Pwt0A6eGn2533+3ubxDduZxvZgacCdwenr8OWBo717qwfTvwgXC8iIjUSRY6/v8Y+EHYbgdeiO3bG8pKlR8D9MYCVr58yLnC/lfC8SIiUieJ9cmY2Y+BdxbZ9SV3vzsc8yXgEHBrUvWohpktB5YDzJgxI82qiIg0lcSCjLv/Xrn9ZvZHwIeAD7i7h+IeYHrssGmhjBLlvwLazGxiuFuJH58/114zmwgcFY4vVtcbgRsBOjo6vNgxIiIycmllly0BPg/8d3c/GNu1EfiOmX0NOB6YDTwCGDA7ZJL1ECUH/L67u5k9CHyMqJ9mGXB37FzLgH8P+zfHgllJ27Zt+w8ze64GbzMJ7wD+I+1KjILqXX+NWnfVu75qWe93FSu0Kq67NWdm3cAk3ryz2OLufxr2fYmon+YQcLm7/yCUnwNcT5TC/C13vyaUv5sowEwBuoA/cPfXzexI4F+B+cB+4CJ3312nt5gIM9vq7h1p12OkVO/6a9S6q971VY96p3InE9KKS+27BrimSPl9wH1FyncTZZ8Vlv8G+PjYaioiImORhewyERFpUgoyjeXGtCswSqp3/TVq3VXv+kq83qn0yYiIyPigOxkREUmMgoyIiCRGQaYBmNkSM9tlZt1mtjLFenzLzF42s5/HyqaY2f1m9nT4fXQoNzO7IdT5cTM7JfacZeH4p81sWax8gZntCM+5oRZzzZnZdDN70MyeMLOdZvYXjVDvcN4jzewRM3ss1P3qUD7LzB4Or7fBzI4I5ZPC4+6wf2bsXKtC+S4zWxwrT+yzFSa37TKzexql3ma2J/xbbjezraGsET4rbWZ2u5k9ZWZPmtnpmam3u+snwz9E44KeAd4NHAE8BpyUUl1+BzgF+Hms7G+AlWF7JfDVsH0O0Zx0BpwGPBzKpwC7w++jw/bRYd8j4VgLzz27BnU+DjglbL+NaNbvk7Je73BeA94atnPAw+F1biMa9wXwTeDPwvZngG+G7YuADWH7pPC5mQTMCp+nlqQ/W8AVwHeAe8LjzNcb2AO8o6CsET4r64A/CdtHAG1ZqXfdL1T6GfGH53RgU+zxKmBVivWZydAgsws4LmwfB+wK2/8IXFx4HHAx8I+x8n8MZccBT8XKhxxXw/rfDXywAes9GfgZsJBohPbEws8HsAk4PWxPDMdZ4Wcmf1ySny2iKZ4eIJol/Z5Qj0ao9x6GB5lMf1aIpsx6lpDIlbV6q7ks+0rNQJ0Vx7r7i2H7l8CxYXukM2q3h+3C8poJzTDzie4IGqLeoclpO/Ay0TpMzzDymcdH+p5q4XqiqaMOh8ejmTE9jXo78CMz22bRxLmQ/c/KLGAf8C+hefKfzewtWam3gozUjEdfczKZE29mbwXuIJqq6NX4vizX290H3H0e0Z3BqcCJKVepIjP7EPCyu29Luy6j8NvufgrRAomfNbPfie/M6GdlIlEz9jfcfT7wa6LmsUFp1ltBJvvKzUydBS+Z2XEA4ffLobxUvcuVTytSPmZmliMKMLe6+52NUu84j5Ynf5CoqajNopnFC19vsI42dObxkb6nsVoEnGdme4jmFTyTaOn0rNcbd+8Jv18G7iIK7Fn/rOwF9rr7w+Hx7URBJxv1rkU7pn6S+yH6lrKb6JY438k5N8X6zGRon8xahnYu/k3YPpehnYuPhPIpRO3HR4efZ4EpYV9h5+I5NaivATcD1xeUZ7re4bxTgbaw3Qr8lGh5jO8xtAP9M2H7swztQL8tbM9laAf6bqLO88Q/W8Dv8mbHf6brDbwFeFts+/8SLQPfCJ+VnwJzwvbqUOdM1DuVC5V+RvwBOocoK+oZokXf0qrHd4EXgX6ib0+XErWdPwA8Dfw49qE04OuhzjuAjth5/phoae1u4FOx8g7g5+E5f09BR+Yo6/zbRM0EjwPbw885Wa93OO/7iGYWfzyc/y9D+bvDf/puogv3pFB+ZHjcHfa/O3auL4X67SKWGZT0Z4uhQSbT9Q71eyz87Myft0E+K/OAreGz0kkUJDJRb00rIyIiiVGfjIiIJEZBRkREEqMgIyIiiVGQERGRxCjIiIhIYhRkRDLCzAbC7L8/N7PvmdnkUP5OM1tvZs+E6U7uM7PfCvt+aGa9+ZmORbJGQUYkO/rcfZ67vxd4A/jTMKX6XcBP3P097r6AaELI/DxUa4FPplNdkcoUZESy6afACcAZQL+7fzO/w90fc/efhu0HgNfSqaJIZQoyIhkT5u86m2g09nuBRpxoUgRQkBHJktYwrf9W4HngppTrIzJmEysfIiJ10ufRtP6DzGwn8LGU6iMyZrqTEcm2zcCk2AJamNn7zOy/pVgnkaopyIhkmEcz2H4E+L2QwrwTuJZopUPM7KdEMxh/wMz2mtni9GorMpxmYRYRkcToTkZERBKjICMiIolRkBERkcQoyIiISGIUZEREJDEKMiIikhgFGRERScz/B7E9UZjrVQk/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(n_components=2) #find 2 principal components\n",
    "pca.fit(X)\n",
    "\n",
    "Y = pca.transform(X)\n",
    "plt.scatter(Y[:,0], Y[:,1])\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are clearly a couple of outliers! This is why we need to normalize the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import normalize\n",
    "X = normalize(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(n_components=2) #find 2 principal components\n",
    "pca.fit(X)\n",
    "\n",
    "Y = pca.transform(X)\n",
    "plt.scatter(Y[:,0], Y[:,1],alpha=0.01)\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then identify clsuters in this data using kmeans."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 0, 3, ..., 3, 3, 1], dtype=int32)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(n_clusters=5)\n",
    "Z = kmeans.fit_predict(X)\n",
    "Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "for i in range(0,5):\n",
    "    rgb = (random.random(), random.random(), random.random(),0.1)\n",
    "    plt.scatter(Y[Z==i,0], Y[Z==i,1],c=rgb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}