ch05 sklearn AgglomerativeClustering scipy.cluster.hierarchy dendrogram, linkage.ipynb

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   "source": [
    "# 05차시 계층적 군집분석(Hierarchical Clustering)\n",
    "\n",
    "## 01 계층적 군집 분석 개요\n",
    "\n",
    "### 계층적 군집 분석의 특징\n",
    "\n",
    "- 데이터간 유사도를 기반으로 계산하며 군집의 개수가 정해져 있지 않음\n",
    "- 계층적 군집분석을 실시하는 과정과 실시 후 특정 군집 개수로 데이터를 라벨링 하는 과정이 있음\n",
    "- 데이터의 변동에 민감하며 학습 데이터가 많을 경우 연산에 많은 시간 소요\n",
    "\n",
    "### 계층도(Dendrogram)\n",
    "\n",
    "- 계층적 군집분석의 산출물 중 하나로 데이터간 거리 기반으로 도식화한 도표\n",
    "- 계층도의 높이는 데이터 또는 군집간 거리에 비례"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b57586f",
   "metadata": {},
   "source": [
    "## 02 주요 함수 및 메서드 소개\n",
    "\n",
    "### sklearn - AgglomerativeClustering()\n",
    "\n",
    "- 계층적 군집분석을 실시할 수 있는 sklearn의 함수\n",
    "- n_clusters에 분리할 군집 개수를 설정\n",
    "- affinity에 데이터 간 거리계산 방법, linkage에 군집 간 유사도 방법 설정\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e8a387aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.cluster import AgglomerativeClustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8be4e8c7",
   "metadata": {
    "scrolled": true
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   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sepal.Length</th>\n",
       "      <th>Sepal.Width</th>\n",
       "      <th>Petal.Length</th>\n",
       "      <th>Petal.Width</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   Sepal.Length  Sepal.Width  Petal.Length  Petal.Width Species\n",
       "0           5.1          3.5           1.4          0.2  setosa\n",
       "1           4.9          3.0           1.4          0.2  setosa\n",
       "2           4.7          3.2           1.3          0.2  setosa\n",
       "3           4.6          3.1           1.5          0.2  setosa\n",
       "4           5.0          3.6           1.4          0.2  setosa"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"실습파일/iris.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0675721d",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sepal.Length</th>\n",
       "      <th>Sepal.Width</th>\n",
       "      <th>Petal.Length</th>\n",
       "      <th>Petal.Width</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   Sepal.Length  Sepal.Width  Petal.Length  Petal.Width\n",
       "0           5.1          3.5           1.4          0.2\n",
       "1           4.9          3.0           1.4          0.2\n",
       "2           4.7          3.2           1.3          0.2\n",
       "3           4.6          3.1           1.5          0.2\n",
       "4           5.0          3.6           1.4          0.2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_sub = df.iloc[:, :-1]\n",
    "df_sub.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8b932fbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AgglomerativeClustering(n_clusters=3)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = AgglomerativeClustering(n_clusters = 3).fit(df_sub)\n",
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0ac27aaf",
   "metadata": {},
   "outputs": [
    {
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       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2,\n",
       "       2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2,\n",
       "       2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0], dtype=int64)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f5e676be",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sepal.Length</th>\n",
       "      <th>Sepal.Width</th>\n",
       "      <th>Petal.Length</th>\n",
       "      <th>Petal.Width</th>\n",
       "      <th>Species</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   Sepal.Length  Sepal.Width  Petal.Length  Petal.Width Species  cluster\n",
       "0           5.1          3.5           1.4          0.2  setosa        1\n",
       "1           4.9          3.0           1.4          0.2  setosa        1\n",
       "2           4.7          3.2           1.3          0.2  setosa        1\n",
       "3           4.6          3.1           1.5          0.2  setosa        1\n",
       "4           5.0          3.6           1.4          0.2  setosa        1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"cluster\"] = model.labels_\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4c302cf6",
   "metadata": {
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   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>cluster</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Species</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>setosa</th>\n",
       "      <td>0</td>\n",
       "      <td>50</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>versicolor</th>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>virginica</th>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "cluster      0   1   2\n",
       "Species               \n",
       "setosa       0  50   0\n",
       "versicolor  49   0   1\n",
       "virginica   15   0  35"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.crosstab(df[\"Species\"], df[\"cluster\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d76cec4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cluster</th>\n",
       "      <th>Sepal.Length</th>\n",
       "      <th>Sepal.Width</th>\n",
       "      <th>Petal.Length</th>\n",
       "      <th>Petal.Width</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>5.920312</td>\n",
       "      <td>2.751562</td>\n",
       "      <td>4.420312</td>\n",
       "      <td>1.434375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.006000</td>\n",
       "      <td>3.428000</td>\n",
       "      <td>1.462000</td>\n",
       "      <td>0.246000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>6.869444</td>\n",
       "      <td>3.086111</td>\n",
       "      <td>5.769444</td>\n",
       "      <td>2.105556</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   cluster  Sepal.Length  Sepal.Width  Petal.Length  Petal.Width\n",
       "0        0      5.920312     2.751562      4.420312     1.434375\n",
       "1        1      5.006000     3.428000      1.462000     0.246000\n",
       "2        2      6.869444     3.086111      5.769444     2.105556"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(\"cluster\").mean().reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e76ba638",
   "metadata": {},
   "source": [
    "### scipy - dendrogram(), linkage()\n",
    "\n",
    "- 계층도(dendrogram)을 그리기 위한 scipy의 함수\n",
    "- linkage() 함수로 데이터 간 거리 계산 및 군집 형성을 실시\n",
    "- dendrogram() 함수로 계층도 시각화"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c90b6fc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.cluster.hierarchy import dendrogram, linkage\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "da5d5302",
   "metadata": {},
   "outputs": [
    {
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       "       [1.28000000e+02, 1.32000000e+02, 1.00000000e-01, 2.00000000e+00],\n",
       "       [1.00000000e+01, 4.80000000e+01, 1.00000000e-01, 2.00000000e+00],\n",
       "       [4.00000000e+00, 3.70000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [1.90000000e+01, 2.10000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [2.90000000e+01, 3.00000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [5.70000000e+01, 9.30000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [8.00000000e+01, 8.10000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [1.16000000e+02, 1.37000000e+02, 1.41421356e-01, 2.00000000e+00],\n",
       "       [8.00000000e+00, 3.80000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [3.00000000e+00, 4.70000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [2.70000000e+01, 2.80000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [8.20000000e+01, 9.20000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [9.50000000e+01, 9.60000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [1.27000000e+02, 1.38000000e+02, 1.41421356e-01, 2.00000000e+00],\n",
       "       [1.00000000e+00, 4.50000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [6.30000000e+01, 9.10000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [6.50000000e+01, 7.50000000e+01, 1.41421356e-01, 2.00000000e+00],\n",
       "       [4.00000000e+01, 1.52000000e+02, 1.73205081e-01, 3.00000000e+00],\n",
       "       [1.23000000e+02, 1.26000000e+02, 1.73205081e-01, 2.00000000e+00],\n",
       "       [4.90000000e+01, 1.51000000e+02, 1.73205081e-01, 3.00000000e+00],\n",
       "       [1.12000000e+02, 1.39000000e+02, 1.73205081e-01, 2.00000000e+00],\n",
       "       [9.40000000e+01, 9.90000000e+01, 1.73205081e-01, 2.00000000e+00],\n",
       "       [1.20000000e+01, 1.68000000e+02, 1.82574186e-01, 3.00000000e+00],\n",
       "       [8.80000000e+01, 1.66000000e+02, 1.82574186e-01, 3.00000000e+00],\n",
       "       [6.60000000e+01, 8.40000000e+01, 2.00000000e-01, 2.00000000e+00],\n",
       "       [2.30000000e+01, 2.60000000e+01, 2.00000000e-01, 2.00000000e+00],\n",
       "       [5.30000000e+01, 8.90000000e+01, 2.00000000e-01, 2.00000000e+00],\n",
       "       [7.40000000e+01, 9.70000000e+01, 2.00000000e-01, 2.00000000e+00],\n",
       "       [2.50000000e+01, 1.53000000e+02, 2.08166600e-01, 3.00000000e+00],\n",
       "       [4.60000000e+01, 1.57000000e+02, 2.16024690e-01, 3.00000000e+00],\n",
       "       [2.00000000e+00, 1.63000000e+02, 2.16024690e-01, 3.00000000e+00],\n",
       "       [1.10000000e+02, 1.47000000e+02, 2.23606798e-01, 2.00000000e+00],\n",
       "       [1.20000000e+02, 1.43000000e+02, 2.23606798e-01, 2.00000000e+00],\n",
       "       [1.36000000e+02, 1.48000000e+02, 2.44948974e-01, 2.00000000e+00],\n",
       "       [7.80000000e+01, 1.69000000e+02, 2.44948974e-01, 3.00000000e+00],\n",
       "       [6.90000000e+01, 1.60000000e+02, 2.44948974e-01, 3.00000000e+00],\n",
       "       [5.40000000e+01, 5.80000000e+01, 2.44948974e-01, 2.00000000e+00],\n",
       "       [1.40000000e+02, 1.44000000e+02, 2.44948974e-01, 2.00000000e+00],\n",
       "       [1.41000000e+02, 1.45000000e+02, 2.44948974e-01, 2.00000000e+00],\n",
       "       [4.30000000e+01, 1.79000000e+02, 2.58198890e-01, 3.00000000e+00],\n",
       "       [6.80000000e+01, 8.70000000e+01, 2.64575131e-01, 2.00000000e+00],\n",
       "       [5.00000000e+01, 5.20000000e+01, 2.64575131e-01, 2.00000000e+00],\n",
       "       [5.10000000e+01, 5.60000000e+01, 2.64575131e-01, 2.00000000e+00],\n",
       "       [1.07000000e+02, 1.30000000e+02, 2.64575131e-01, 2.00000000e+00],\n",
       "       [1.05000000e+02, 1.22000000e+02, 2.64575131e-01, 2.00000000e+00],\n",
       "       [1.03000000e+02, 1.61000000e+02, 2.70801280e-01, 3.00000000e+00],\n",
       "       [1.64000000e+02, 1.71000000e+02, 2.75680975e-01, 5.00000000e+00],\n",
       "       [2.00000000e+01, 3.10000000e+01, 2.82842712e-01, 2.00000000e+00],\n",
       "       [1.10000000e+01, 1.58000000e+02, 2.94392029e-01, 3.00000000e+00],\n",
       "       [6.70000000e+01, 1.65000000e+02, 2.94392029e-01, 3.00000000e+00],\n",
       "       [7.00000000e+01, 1.67000000e+02, 2.94392029e-01, 3.00000000e+00],\n",
       "       [4.20000000e+01, 1.62000000e+02, 2.94392029e-01, 3.00000000e+00],\n",
       "       [1.13000000e+02, 1.50000000e+02, 3.05505046e-01, 3.00000000e+00],\n",
       "       [6.00000000e+00, 1.84000000e+02, 3.13581462e-01, 4.00000000e+00],\n",
       "       [1.73000000e+02, 2.00000000e+02, 3.14642654e-01, 8.00000000e+00],\n",
       "       [5.50000000e+01, 9.00000000e+01, 3.16227766e-01, 2.00000000e+00],\n",
       "       [1.76000000e+02, 1.82000000e+02, 3.16227766e-01, 6.00000000e+00],\n",
       "       [8.60000000e+01, 1.95000000e+02, 3.21455025e-01, 3.00000000e+00],\n",
       "       [1.24000000e+02, 1.86000000e+02, 3.31662479e-01, 3.00000000e+00],\n",
       "       [8.30000000e+01, 1.33000000e+02, 3.31662479e-01, 2.00000000e+00],\n",
       "       [5.00000000e+00, 1.80000000e+01, 3.31662479e-01, 2.00000000e+00],\n",
       "       [1.30000000e+01, 2.05000000e+02, 3.36650165e-01, 4.00000000e+00],\n",
       "       [1.75000000e+02, 1.77000000e+02, 3.41565026e-01, 5.00000000e+00],\n",
       "       [3.20000000e+01, 3.30000000e+01, 3.46410162e-01, 2.00000000e+00],\n",
       "       [1.25000000e+02, 1.29000000e+02, 3.46410162e-01, 2.00000000e+00],\n",
       "       [1.04000000e+02, 1.54000000e+02, 3.51188458e-01, 3.00000000e+00],\n",
       "       [7.30000000e+01, 1.88000000e+02, 3.53553391e-01, 4.00000000e+00],\n",
       "       [1.49000000e+02, 2.04000000e+02, 3.58236421e-01, 4.00000000e+00],\n",
       "       [1.46000000e+02, 1.72000000e+02, 3.60555128e-01, 3.00000000e+00],\n",
       "       [1.21000000e+02, 2.06000000e+02, 3.62859018e-01, 4.00000000e+00],\n",
       "       [3.60000000e+01, 1.55000000e+02, 3.69684550e-01, 3.00000000e+00],\n",
       "       [7.60000000e+01, 1.90000000e+02, 3.74165739e-01, 3.00000000e+00],\n",
       "       [1.15000000e+02, 1.87000000e+02, 3.74165739e-01, 3.00000000e+00],\n",
       "       [6.10000000e+01, 7.10000000e+01, 4.00000000e-01, 2.00000000e+00],\n",
       "       [1.56000000e+02, 2.08000000e+02, 4.06201920e-01, 1.00000000e+01],\n",
       "       [7.20000000e+01, 2.13000000e+02, 4.12310563e-01, 3.00000000e+00],\n",
       "       [1.17000000e+02, 1.31000000e+02, 4.12310563e-01, 2.00000000e+00],\n",
       "       [1.91000000e+02, 2.12000000e+02, 4.14728827e-01, 5.00000000e+00],\n",
       "       [2.40000000e+01, 2.02000000e+02, 4.22295315e-01, 4.00000000e+00],\n",
       "       [9.80000000e+01, 1.59000000e+02, 4.39696865e-01, 3.00000000e+00],\n",
       "       [1.60000000e+01, 2.24000000e+02, 4.39696865e-01, 4.00000000e+00],\n",
       "       [3.50000000e+01, 2.10000000e+02, 4.39696865e-01, 7.00000000e+00],\n",
       "       [6.40000000e+01, 7.90000000e+01, 4.47213595e-01, 2.00000000e+00],\n",
       "       [8.50000000e+01, 1.96000000e+02, 4.58257569e-01, 3.00000000e+00],\n",
       "       [7.70000000e+01, 1.85000000e+02, 4.65474668e-01, 3.00000000e+00],\n",
       "       [4.40000000e+01, 1.83000000e+02, 4.67261526e-01, 4.00000000e+00],\n",
       "       [1.11000000e+02, 1.99000000e+02, 4.81317636e-01, 4.00000000e+00],\n",
       "       [1.80000000e+02, 1.89000000e+02, 4.81663783e-01, 5.00000000e+00],\n",
       "       [1.02000000e+02, 2.18000000e+02, 4.89897949e-01, 3.00000000e+00],\n",
       "       [1.74000000e+02, 1.92000000e+02, 5.14781507e-01, 4.00000000e+00],\n",
       "       [1.81000000e+02, 2.27000000e+02, 5.29150262e-01, 4.00000000e+00],\n",
       "       [1.70000000e+02, 2.25000000e+02, 5.32916504e-01, 5.00000000e+00],\n",
       "       [1.18000000e+02, 1.98000000e+02, 5.38516481e-01, 3.00000000e+00],\n",
       "       [1.40000000e+01, 1.50000000e+01, 5.47722558e-01, 2.00000000e+00],\n",
       "       [1.78000000e+02, 2.09000000e+02, 5.74456265e-01, 4.00000000e+00],\n",
       "       [2.22000000e+02, 2.29000000e+02, 5.80229840e-01, 6.00000000e+00],\n",
       "       [2.01000000e+02, 2.34000000e+02, 5.94418483e-01, 6.00000000e+00],\n",
       "       [1.14000000e+02, 2.23000000e+02, 6.05805249e-01, 5.00000000e+00],\n",
       "       [6.00000000e+01, 2.33000000e+02, 6.13731755e-01, 4.00000000e+00],\n",
       "       [2.17000000e+02, 2.47000000e+02, 6.24499800e-01, 4.00000000e+00],\n",
       "       [5.90000000e+01, 2.41000000e+02, 6.30872412e-01, 6.00000000e+00],\n",
       "       [2.07000000e+02, 2.32000000e+02, 6.36396103e-01, 8.00000000e+00],\n",
       "       [1.97000000e+02, 2.42000000e+02, 6.40312424e-01, 5.00000000e+00],\n",
       "       [6.20000000e+01, 2.03000000e+02, 6.42910051e-01, 4.00000000e+00],\n",
       "       [2.14000000e+02, 2.50000000e+02, 6.62696512e-01, 8.00000000e+00],\n",
       "       [1.19000000e+02, 1.94000000e+02, 7.09459888e-01, 3.00000000e+00],\n",
       "       [1.00000000e+02, 2.26000000e+02, 7.24568837e-01, 4.00000000e+00],\n",
       "       [1.08000000e+02, 2.19000000e+02, 7.32575366e-01, 4.00000000e+00],\n",
       "       [2.16000000e+02, 2.48000000e+02, 7.34090518e-01, 9.00000000e+00],\n",
       "       [2.11000000e+02, 2.45000000e+02, 7.34960316e-01, 8.00000000e+00],\n",
       "       [2.40000000e+02, 2.61000000e+02, 7.63216876e-01, 8.00000000e+00],\n",
       "       [1.93000000e+02, 2.39000000e+02, 7.76285416e-01, 7.00000000e+00],\n",
       "       [1.09000000e+02, 1.35000000e+02, 8.06225775e-01, 2.00000000e+00],\n",
       "       [2.35000000e+02, 2.55000000e+02, 8.18738868e-01, 1.50000000e+01],\n",
       "       [2.38000000e+02, 2.43000000e+02, 8.21873585e-01, 7.00000000e+00],\n",
       "       [2.36000000e+02, 2.54000000e+02, 8.26135582e-01, 8.00000000e+00],\n",
       "       [2.20000000e+01, 2.15000000e+02, 8.55569985e-01, 5.00000000e+00],\n",
       "       [2.20000000e+02, 2.44000000e+02, 8.64580823e-01, 8.00000000e+00],\n",
       "       [2.28000000e+02, 2.65000000e+02, 9.09981993e-01, 1.70000000e+01],\n",
       "       [2.57000000e+02, 2.69000000e+02, 9.28708781e-01, 1.20000000e+01],\n",
       "       [1.34000000e+02, 2.49000000e+02, 9.29157324e-01, 7.00000000e+00],\n",
       "       [2.21000000e+02, 2.37000000e+02, 1.00534287e+00, 7.00000000e+00],\n",
       "       [2.31000000e+02, 2.60000000e+02, 1.04705937e+00, 9.00000000e+00],\n",
       "       [4.10000000e+01, 2.70000000e+02, 1.10513951e+00, 6.00000000e+00],\n",
       "       [2.30000000e+02, 2.66000000e+02, 1.15325626e+00, 4.00000000e+00],\n",
       "       [1.06000000e+02, 2.62000000e+02, 1.21700908e+00, 1.00000000e+01],\n",
       "       [2.53000000e+02, 2.58000000e+02, 1.25399362e+00, 1.20000000e+01],\n",
       "       [2.59000000e+02, 2.74000000e+02, 1.30486270e+00, 1.00000000e+01],\n",
       "       [2.67000000e+02, 2.77000000e+02, 1.37126983e+00, 2.10000000e+01],\n",
       "       [2.64000000e+02, 2.68000000e+02, 1.41139074e+00, 1.50000000e+01],\n",
       "       [2.71000000e+02, 2.75000000e+02, 1.49547731e+00, 1.50000000e+01],\n",
       "       [2.46000000e+02, 2.78000000e+02, 1.59776630e+00, 7.00000000e+00],\n",
       "       [2.51000000e+02, 2.81000000e+02, 1.75916647e+00, 1.50000000e+01],\n",
       "       [2.76000000e+02, 2.83000000e+02, 1.76044502e+00, 2.40000000e+01],\n",
       "       [2.56000000e+02, 2.85000000e+02, 1.84584475e+00, 1.20000000e+01],\n",
       "       [2.73000000e+02, 2.79000000e+02, 1.91608028e+00, 2.20000000e+01],\n",
       "       [2.72000000e+02, 2.80000000e+02, 1.91875287e+00, 2.90000000e+01],\n",
       "       [2.63000000e+02, 2.84000000e+02, 2.05363058e+00, 2.30000000e+01],\n",
       "       [2.52000000e+02, 2.89000000e+02, 2.81393883e+00, 2.60000000e+01],\n",
       "       [2.86000000e+02, 2.91000000e+02, 2.86941764e+00, 3.80000000e+01],\n",
       "       [2.82000000e+02, 2.90000000e+02, 3.82805262e+00, 5.00000000e+01],\n",
       "       [2.87000000e+02, 2.88000000e+02, 4.84770851e+00, 3.60000000e+01],\n",
       "       [2.92000000e+02, 2.93000000e+02, 6.39940682e+00, 6.40000000e+01],\n",
       "       [2.95000000e+02, 2.96000000e+02, 1.23003961e+01, 1.00000000e+02],\n",
       "       [2.94000000e+02, 2.97000000e+02, 3.24476070e+01, 1.50000000e+02]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "link = linkage(df_sub, method = \"ward\")\n",
    "link"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e543ff0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "dendrogram(link)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f67efc0",
   "metadata": {},
   "source": [
    "## Q1 당뇨병 여부(Outcome) 변수를 제외한 나머지 변수를 입력으로 하고 계층적 군집분석을 실시했을 때 3번 군집의 인슐린(Insulin) 평균은?\n",
    "1) 4개의 군집으로 Ward, Euclidean 방법 사용"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "812e954c",
   "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>Pregnancies</th>\n",
       "      <th>Glucose</th>\n",
       "      <th>BloodPressure</th>\n",
       "      <th>SkinThickness</th>\n",
       "      <th>Insulin</th>\n",
       "      <th>BMI</th>\n",
       "      <th>DiabetesPedigreeFunction</th>\n",
       "      <th>Age</th>\n",
       "      <th>Outcome</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>148</td>\n",
       "      <td>72</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>33.6</td>\n",
       "      <td>0.627</td>\n",
       "      <td>50</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>85</td>\n",
       "      <td>66</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>26.6</td>\n",
       "      <td>0.351</td>\n",
       "      <td>31</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8</td>\n",
       "      <td>183</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>23.3</td>\n",
       "      <td>0.672</td>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>89</td>\n",
       "      <td>66</td>\n",
       "      <td>23</td>\n",
       "      <td>94</td>\n",
       "      <td>28.1</td>\n",
       "      <td>0.167</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>137</td>\n",
       "      <td>40</td>\n",
       "      <td>35</td>\n",
       "      <td>168</td>\n",
       "      <td>43.1</td>\n",
       "      <td>2.288</td>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Pregnancies  Glucose  BloodPressure  SkinThickness  Insulin   BMI  \\\n",
       "0            6      148             72             35        0  33.6   \n",
       "1            1       85             66             29        0  26.6   \n",
       "2            8      183             64              0        0  23.3   \n",
       "3            1       89             66             23       94  28.1   \n",
       "4            0      137             40             35      168  43.1   \n",
       "\n",
       "   DiabetesPedigreeFunction  Age  Outcome  \n",
       "0                     0.627   50        1  \n",
       "1                     0.351   31        0  \n",
       "2                     0.672   32        1  \n",
       "3                     0.167   21        0  \n",
       "4                     2.288   33        1  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1 = pd.read_csv(\"실습파일/diabetes.csv\")\n",
    "Q1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b164e644",
   "metadata": {
    "scrolled": true
   },
   "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>Pregnancies</th>\n",
       "      <th>Glucose</th>\n",
       "      <th>BloodPressure</th>\n",
       "      <th>SkinThickness</th>\n",
       "      <th>Insulin</th>\n",
       "      <th>BMI</th>\n",
       "      <th>DiabetesPedigreeFunction</th>\n",
       "      <th>Age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>148</td>\n",
       "      <td>72</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>33.6</td>\n",
       "      <td>0.627</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>85</td>\n",
       "      <td>66</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>26.6</td>\n",
       "      <td>0.351</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8</td>\n",
       "      <td>183</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>23.3</td>\n",
       "      <td>0.672</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>89</td>\n",
       "      <td>66</td>\n",
       "      <td>23</td>\n",
       "      <td>94</td>\n",
       "      <td>28.1</td>\n",
       "      <td>0.167</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>137</td>\n",
       "      <td>40</td>\n",
       "      <td>35</td>\n",
       "      <td>168</td>\n",
       "      <td>43.1</td>\n",
       "      <td>2.288</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Pregnancies  Glucose  BloodPressure  SkinThickness  Insulin   BMI  \\\n",
       "0            6      148             72             35        0  33.6   \n",
       "1            1       85             66             29        0  26.6   \n",
       "2            8      183             64              0        0  23.3   \n",
       "3            1       89             66             23       94  28.1   \n",
       "4            0      137             40             35      168  43.1   \n",
       "\n",
       "   DiabetesPedigreeFunction  Age  \n",
       "0                     0.627   50  \n",
       "1                     0.351   31  \n",
       "2                     0.672   32  \n",
       "3                     0.167   21  \n",
       "4                     2.288   33  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1_sub = Q1.iloc[:, :-1]\n",
    "Q1_sub.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f94d4de4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AgglomerativeClustering(n_clusters=4)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = AgglomerativeClustering(n_clusters = 4).fit(Q1_sub)\n",
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "84463bd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Pregnancies</th>\n",
       "      <th>Glucose</th>\n",
       "      <th>BloodPressure</th>\n",
       "      <th>SkinThickness</th>\n",
       "      <th>Insulin</th>\n",
       "      <th>BMI</th>\n",
       "      <th>DiabetesPedigreeFunction</th>\n",
       "      <th>Age</th>\n",
       "      <th>Outcome</th>\n",
       "      <th>cluster</th>\n",
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       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>148</td>\n",
       "      <td>72</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>33.6</td>\n",
       "      <td>0.627</td>\n",
       "      <td>50</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>85</td>\n",
       "      <td>66</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>26.6</td>\n",
       "      <td>0.351</td>\n",
       "      <td>31</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8</td>\n",
       "      <td>183</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>23.3</td>\n",
       "      <td>0.672</td>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>89</td>\n",
       "      <td>66</td>\n",
       "      <td>23</td>\n",
       "      <td>94</td>\n",
       "      <td>28.1</td>\n",
       "      <td>0.167</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>137</td>\n",
       "      <td>40</td>\n",
       "      <td>35</td>\n",
       "      <td>168</td>\n",
       "      <td>43.1</td>\n",
       "      <td>2.288</td>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Pregnancies  Glucose  BloodPressure  SkinThickness  Insulin   BMI  \\\n",
       "0            6      148             72             35        0  33.6   \n",
       "1            1       85             66             29        0  26.6   \n",
       "2            8      183             64              0        0  23.3   \n",
       "3            1       89             66             23       94  28.1   \n",
       "4            0      137             40             35      168  43.1   \n",
       "\n",
       "   DiabetesPedigreeFunction  Age  Outcome  cluster  \n",
       "0                     0.627   50        1        1  \n",
       "1                     0.351   31        0        1  \n",
       "2                     0.672   32        1        1  \n",
       "3                     0.167   21        0        3  \n",
       "4                     2.288   33        1        0  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1[\"cluster\"] = model.labels_\n",
    "Q1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "74026f6b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <th>Insulin</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>548.833333</td>\n",
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       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>85.050000</td>\n",
       "    </tr>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   cluster     Insulin\n",
       "0        0  207.018182\n",
       "1        1    0.620779\n",
       "2        2  548.833333\n",
       "3        3   85.050000"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1.groupby(\"cluster\")[\"Insulin\"].mean().reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4716c8a3",
   "metadata": {},
   "source": [
    "## Q2 당뇨병 여부(Outcome) 변수를 제외한 나머지 변수를 입력으로 하고 계층적 군집분석을 실시했을 때 6개의 군집으로 분할하는 경우 군집 개수가 가장 큰 군집의 행 개수는?\n",
    "1) Pregnancies가 0이면서 BMI가 0보다 큰 데이터만 사용"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "78c7e8bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40.5</td>\n",
       "      <td>1.781</td>\n",
       "      <td>44</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",
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       "      <th>713</th>\n",
       "      <td>0</td>\n",
       "      <td>134</td>\n",
       "      <td>58</td>\n",
       "      <td>20</td>\n",
       "      <td>291</td>\n",
       "      <td>26.4</td>\n",
       "      <td>0.352</td>\n",
       "      <td>21</td>\n",
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       "      <th>727</th>\n",
       "      <td>0</td>\n",
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       "      <td>84</td>\n",
       "      <td>26</td>\n",
       "      <td>0</td>\n",
       "      <td>32.4</td>\n",
       "      <td>0.433</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>736</th>\n",
       "      <td>0</td>\n",
       "      <td>126</td>\n",
       "      <td>86</td>\n",
       "      <td>27</td>\n",
       "      <td>120</td>\n",
       "      <td>27.4</td>\n",
       "      <td>0.515</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>753</th>\n",
       "      <td>0</td>\n",
       "      <td>181</td>\n",
       "      <td>88</td>\n",
       "      <td>44</td>\n",
       "      <td>510</td>\n",
       "      <td>43.3</td>\n",
       "      <td>0.222</td>\n",
       "      <td>26</td>\n",
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       "    <tr>\n",
       "      <th>757</th>\n",
       "      <td>0</td>\n",
       "      <td>123</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>36.3</td>\n",
       "      <td>0.258</td>\n",
       "      <td>52</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>108 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Pregnancies  Glucose  BloodPressure  SkinThickness  Insulin   BMI  \\\n",
       "4              0      137             40             35      168  43.1   \n",
       "16             0      118             84             47      230  45.8   \n",
       "45             0      180             66             39        0  42.0   \n",
       "57             0      100             88             60      110  46.8   \n",
       "58             0      146             82              0        0  40.5   \n",
       "..           ...      ...            ...            ...      ...   ...   \n",
       "713            0      134             58             20      291  26.4   \n",
       "727            0      141             84             26        0  32.4   \n",
       "736            0      126             86             27      120  27.4   \n",
       "753            0      181             88             44      510  43.3   \n",
       "757            0      123             72              0        0  36.3   \n",
       "\n",
       "     DiabetesPedigreeFunction  Age  \n",
       "4                       2.288   33  \n",
       "16                      0.551   31  \n",
       "45                      1.893   25  \n",
       "57                      0.962   31  \n",
       "58                      1.781   44  \n",
       "..                        ...  ...  \n",
       "713                     0.352   21  \n",
       "727                     0.433   22  \n",
       "736                     0.515   21  \n",
       "753                     0.222   26  \n",
       "757                     0.258   52  \n",
       "\n",
       "[108 rows x 8 columns]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2_sub = Q1_sub.loc[(Q1_sub[\"Pregnancies\"] == 0) & (Q1_sub[\"BMI\"] > 0)]\n",
    "Q2_sub"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "28a91c05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3, 0, 1, 0, 1, 0, 4, 0, 0, 1, 1, 0, 0, 1, 1, 0, 5, 0, 1, 1, 0,\n",
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     "execution_count": 30,
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     "output_type": "execute_result"
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   ],
   "source": [
    "Q2_model = AgglomerativeClustering(n_clusters = 6).fit(Q2_sub)\n",
    "Q2_model.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d71766cc",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\jtkim\\AppData\\Local\\Temp\\ipykernel_29124\\2297706429.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  Q2_sub[\"cluster\"] = Q2_model.labels_\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0    44\n",
       "1    33\n",
       "3    13\n",
       "4     9\n",
       "5     6\n",
       "2     3\n",
       "Name: cluster, dtype: int64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2_sub[\"cluster\"] = Q2_model.labels_\n",
    "Q2_sub[\"cluster\"].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "853b7d9f",
   "metadata": {},
   "source": [
    "## Q3 당뇨병 여부(Outcome) 변수를 제외한 나머지 변수를 입력으로 하고 계층적 군집분석을 실시했을 때 6개의 군집으로 분할하는 경우 1번과 2번 군집의 유클리드 거리는 얼마인가?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "83c8bc96",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>28.1</td>\n",
       "      <td>0.167</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>137</td>\n",
       "      <td>40</td>\n",
       "      <td>35</td>\n",
       "      <td>168</td>\n",
       "      <td>43.1</td>\n",
       "      <td>2.288</td>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Pregnancies  Glucose  BloodPressure  SkinThickness  Insulin   BMI  \\\n",
       "0            6      148             72             35        0  33.6   \n",
       "1            1       85             66             29        0  26.6   \n",
       "2            8      183             64              0        0  23.3   \n",
       "3            1       89             66             23       94  28.1   \n",
       "4            0      137             40             35      168  43.1   \n",
       "\n",
       "   DiabetesPedigreeFunction  Age  Outcome  \n",
       "0                     0.627   50        1  \n",
       "1                     0.351   31        0  \n",
       "2                     0.672   32        1  \n",
       "3                     0.167   21        0  \n",
       "4                     2.288   33        1  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3 = pd.read_csv(\"실습파일/diabetes.csv\")\n",
    "Q3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "2e33edd9",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "    Pregnancies  Glucose  BloodPressure  SkinThickness  Insulin   BMI  \\\n",
       "4             0      137             40             35      168  43.1   \n",
       "16            0      118             84             47      230  45.8   \n",
       "45            0      180             66             39        0  42.0   \n",
       "57            0      100             88             60      110  46.8   \n",
       "58            0      146             82              0        0  40.5   \n",
       "\n",
       "    DiabetesPedigreeFunction  Age  \n",
       "4                      2.288   33  \n",
       "16                     0.551   31  \n",
       "45                     1.893   25  \n",
       "57                     0.962   31  \n",
       "58                     1.781   44  "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3_sub = Q3.loc[(Q3[\"Pregnancies\"] == 0) & (Q3[\"BMI\"] > 0), :\"Age\"]\n",
    "Q3_sub.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "398f8346",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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      "text/plain": [
       "    Pregnancies  Glucose  BloodPressure  SkinThickness  Insulin   BMI  \\\n",
       "4             0      137             40             35      168  43.1   \n",
       "16            0      118             84             47      230  45.8   \n",
       "45            0      180             66             39        0  42.0   \n",
       "57            0      100             88             60      110  46.8   \n",
       "58            0      146             82              0        0  40.5   \n",
       "\n",
       "    DiabetesPedigreeFunction  Age  cluster  \n",
       "4                      2.288   33        3  \n",
       "16                     0.551   31        3  \n",
       "45                     1.893   25        0  \n",
       "57                     0.962   31        1  \n",
       "58                     1.781   44        0  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3_model = AgglomerativeClustering(n_clusters = 6).fit(Q3_sub)\n",
    "Q3_sub[\"cluster\"] = Q3_model.labels_\n",
    "Q3_sub.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "d472c441",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "   cluster  Pregnancies     Glucose  BloodPressure  SkinThickness     Insulin  \\\n",
       "0        0          0.0  122.840909      74.886364      15.795455    0.318182   \n",
       "1        1          0.0  109.121212      74.666667      30.939394   94.424242   \n",
       "2        2          0.0  174.333333      79.333333      35.333333  556.000000   \n",
       "3        3          0.0  134.153846      67.538462      31.076923  195.153846   \n",
       "4        4          0.0  125.555556       0.000000       0.000000    0.000000   \n",
       "5        5          0.0  156.000000      73.333333      33.333333  273.666667   \n",
       "\n",
       "         BMI  DiabetesPedigreeFunction        Age  \n",
       "0  32.659091                  0.508614  31.000000  \n",
       "1  36.978788                  0.455333  24.060606  \n",
       "2  43.400000                  0.573667  23.333333  \n",
       "3  35.400000                  0.682615  25.076923  \n",
       "4  34.522222                  0.505000  28.444444  \n",
       "5  41.300000                  0.451500  31.166667  "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "Q3_cl = Q3_sub.groupby(\"cluster\").mean().reset_index()\n",
    "Q3_cl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "7e8a86dc",
   "metadata": {
    "scrolled": true
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   "outputs": [
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      "text/plain": [
       "   Pregnancies     Glucose  BloodPressure  SkinThickness     Insulin  \\\n",
       "0          0.0  122.840909      74.886364      15.795455    0.318182   \n",
       "1          0.0  109.121212      74.666667      30.939394   94.424242   \n",
       "2          0.0  174.333333      79.333333      35.333333  556.000000   \n",
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       "4          0.0  125.555556       0.000000       0.000000    0.000000   \n",
       "5          0.0  156.000000      73.333333      33.333333  273.666667   \n",
       "\n",
       "         BMI  DiabetesPedigreeFunction        Age  \n",
       "0  32.659091                  0.508614  31.000000  \n",
       "1  36.978788                  0.455333  24.060606  \n",
       "2  43.400000                  0.573667  23.333333  \n",
       "3  35.400000                  0.682615  25.076923  \n",
       "4  34.522222                  0.505000  28.444444  \n",
       "5  41.300000                  0.451500  31.166667  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3_cl = Q3_cl.iloc[:, 1:]\n",
    "Q3_cl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "5165e059",
   "metadata": {},
   "outputs": [
    {
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       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Pregnancies</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Glucose</th>\n",
       "      <td>122.840909</td>\n",
       "      <td>109.121212</td>\n",
       "      <td>174.333333</td>\n",
       "      <td>134.153846</td>\n",
       "      <td>125.555556</td>\n",
       "      <td>156.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BloodPressure</th>\n",
       "      <td>74.886364</td>\n",
       "      <td>74.666667</td>\n",
       "      <td>79.333333</td>\n",
       "      <td>67.538462</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>73.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SkinThickness</th>\n",
       "      <td>15.795455</td>\n",
       "      <td>30.939394</td>\n",
       "      <td>35.333333</td>\n",
       "      <td>31.076923</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>33.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Insulin</th>\n",
       "      <td>0.318182</td>\n",
       "      <td>94.424242</td>\n",
       "      <td>556.000000</td>\n",
       "      <td>195.153846</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>273.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BMI</th>\n",
       "      <td>32.659091</td>\n",
       "      <td>36.978788</td>\n",
       "      <td>43.400000</td>\n",
       "      <td>35.400000</td>\n",
       "      <td>34.522222</td>\n",
       "      <td>41.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DiabetesPedigreeFunction</th>\n",
       "      <td>0.508614</td>\n",
       "      <td>0.455333</td>\n",
       "      <td>0.573667</td>\n",
       "      <td>0.682615</td>\n",
       "      <td>0.505000</td>\n",
       "      <td>0.451500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age</th>\n",
       "      <td>31.000000</td>\n",
       "      <td>24.060606</td>\n",
       "      <td>23.333333</td>\n",
       "      <td>25.076923</td>\n",
       "      <td>28.444444</td>\n",
       "      <td>31.166667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                   0           1           2           3  \\\n",
       "Pregnancies                 0.000000    0.000000    0.000000    0.000000   \n",
       "Glucose                   122.840909  109.121212  174.333333  134.153846   \n",
       "BloodPressure              74.886364   74.666667   79.333333   67.538462   \n",
       "SkinThickness              15.795455   30.939394   35.333333   31.076923   \n",
       "Insulin                     0.318182   94.424242  556.000000  195.153846   \n",
       "BMI                        32.659091   36.978788   43.400000   35.400000   \n",
       "DiabetesPedigreeFunction    0.508614    0.455333    0.573667    0.682615   \n",
       "Age                        31.000000   24.060606   23.333333   25.076923   \n",
       "\n",
       "                                   4           5  \n",
       "Pregnancies                 0.000000    0.000000  \n",
       "Glucose                   125.555556  156.000000  \n",
       "BloodPressure               0.000000   73.333333  \n",
       "SkinThickness               0.000000   33.333333  \n",
       "Insulin                     0.000000  273.666667  \n",
       "BMI                        34.522222   41.300000  \n",
       "DiabetesPedigreeFunction    0.505000    0.451500  \n",
       "Age                        28.444444   31.166667  "
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3_cl_t = Q3_cl.transpose()\n",
    "Q3_cl_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "2f74c216",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>diff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Pregnancies</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Glucose</th>\n",
       "      <td>122.840909</td>\n",
       "      <td>109.121212</td>\n",
       "      <td>174.333333</td>\n",
       "      <td>134.153846</td>\n",
       "      <td>125.555556</td>\n",
       "      <td>156.000000</td>\n",
       "      <td>-65.212121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BloodPressure</th>\n",
       "      <td>74.886364</td>\n",
       "      <td>74.666667</td>\n",
       "      <td>79.333333</td>\n",
       "      <td>67.538462</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>73.333333</td>\n",
       "      <td>-4.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SkinThickness</th>\n",
       "      <td>15.795455</td>\n",
       "      <td>30.939394</td>\n",
       "      <td>35.333333</td>\n",
       "      <td>31.076923</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>33.333333</td>\n",
       "      <td>-4.393939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Insulin</th>\n",
       "      <td>0.318182</td>\n",
       "      <td>94.424242</td>\n",
       "      <td>556.000000</td>\n",
       "      <td>195.153846</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>273.666667</td>\n",
       "      <td>-461.575758</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        0           1           2           3           4  \\\n",
       "Pregnancies      0.000000    0.000000    0.000000    0.000000    0.000000   \n",
       "Glucose        122.840909  109.121212  174.333333  134.153846  125.555556   \n",
       "BloodPressure   74.886364   74.666667   79.333333   67.538462    0.000000   \n",
       "SkinThickness   15.795455   30.939394   35.333333   31.076923    0.000000   \n",
       "Insulin          0.318182   94.424242  556.000000  195.153846    0.000000   \n",
       "\n",
       "                        5        diff  \n",
       "Pregnancies      0.000000    0.000000  \n",
       "Glucose        156.000000  -65.212121  \n",
       "BloodPressure   73.333333   -4.666667  \n",
       "SkinThickness   33.333333   -4.393939  \n",
       "Insulin        273.666667 -461.575758  "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3_cl_t[\"diff\"] = Q3_cl_t[1] - Q3_cl_t[2] # 여기서 1, 2는 변수명임\n",
    "Q3_cl_t.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "be929577",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "466.248496093336"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(Q3_cl_t[\"diff\"] ** 2).sum() ** 0.5"
   ]
  }
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