DeepLearning_Assignment8.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Representation Learning Assignment\n",
    "We have learned the importance of representation. Let's try the example to understand better. Here is the code to produce the data similar to the example we used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a2a81dac8>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD3CAYAAADmBxSSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\naGholCG0cNfQ0NAoQ/z/gfG6vxtYobAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1100d2cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n",
    "\n",
    "%matplotlib inline  \n",
    "\n",
    "PI=np.pi\n",
    "PI2=2*PI\n",
    "\n",
    "def gencircle(rc,rr=0.1,offset=[0,0],num=100,label=0):\n",
    "    #taken from https://qiita.com/xiangze750/items/1d024c8536d128c3ceae\n",
    "    c=[]\n",
    "    for i in range(num):\n",
    "        r=rc+np.random.uniform(-rr,rr,1)\n",
    "        th=np.random.uniform(0,PI2,1)\n",
    "        c.append([r*np.sin(th)+offset[0],r*np.cos(th)+offset[1]])\n",
    "    return np.c_[np.array(c).reshape(num,2),np.repeat(label,num)]\n",
    "\n",
    "X=np.r_[gencircle(0.1,0.1,num=1000,label=0),gencircle(0.5,0.1,num=1000,label=1)][:,0:2]\n",
    "\n",
    "plt.scatter(X[0:1000,0],X[0:1000,1],color=\"red\")\n",
    "plt.scatter(X[1000:2000,0],X[1000:2000,1],color=\"blue\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.03597942, -0.01794801],\n",
       "       [ 0.11680984,  0.09680496],\n",
       "       [-0.00333146,  0.00382334],\n",
       "       ..., \n",
       "       [ 0.43523319,  0.34139888],\n",
       "       [ 0.21996141,  0.44369549],\n",
       "       [ 0.29156638,  0.38797451]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.035979</td>\n",
       "      <td>-0.017948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.116810</td>\n",
       "      <td>0.096805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.003331</td>\n",
       "      <td>0.003823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.002850</td>\n",
       "      <td>-0.021912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.018157</td>\n",
       "      <td>0.063400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1\n",
       "0 -0.035979 -0.017948\n",
       "1  0.116810  0.096805\n",
       "2 -0.003331  0.003823\n",
       "3 -0.002850 -0.021912\n",
       "4 -0.018157  0.063400"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mydata = pd.DataFrame(X)\n",
    "mydata.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Red = 0, Blue = 1\n",
    "mydata['Color'] = 0\n",
    "mydata.loc[1000:2000,('Color')] = 1\n",
    "mydata.columns = ['Xcoord', 'Ycoord', 'Color']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Xcoord</th>\n",
       "      <th>Ycoord</th>\n",
       "      <th>Color</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.035979</td>\n",
       "      <td>-0.017948</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.116810</td>\n",
       "      <td>0.096805</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.003331</td>\n",
       "      <td>0.003823</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.002850</td>\n",
       "      <td>-0.021912</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.018157</td>\n",
       "      <td>0.063400</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Xcoord    Ycoord  Color\n",
       "0 -0.035979 -0.017948      0\n",
       "1  0.116810  0.096805      0\n",
       "2 -0.003331  0.003823      0\n",
       "3 -0.002850 -0.021912      0\n",
       "4 -0.018157  0.063400      0"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mydata.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0]\n",
      " [0]\n",
      " [0]\n",
      " ..., \n",
      " [1]\n",
      " [1]\n",
      " [1]]\n",
      "[[-0.03597942 -0.01794801]\n",
      " [ 0.11680984  0.09680496]\n",
      " [-0.00333146  0.00382334]\n",
      " ..., \n",
      " [ 0.43523319  0.34139888]\n",
      " [ 0.21996141  0.44369549]\n",
      " [ 0.29156638  0.38797451]]\n"
     ]
    }
   ],
   "source": [
    "y = mydata.drop(labels = ['Xcoord', 'Ycoord'], axis=1).values\n",
    "X = mydata.drop(labels = ['Color'], axis=1).values\n",
    "print(y)\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "# set seed for numpy and tensorflow\n",
    "# set for reproducible results\n",
    "seed = 5\n",
    "np.random.seed(seed)\n",
    "tf.set_random_seed(seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you see,  X  is a matrix whose shape is  2000×2  the first 1000 rows are corresponding to red points, and the second 1000 row are corresponding to the blue data points.\n",
    "\n",
    "# Task\n",
    "* Try logistic regression to classify the data. It's okay if it does not work.\n",
    "* Try feed forward neural network to classify the data. For this one, you need to find the architecture that works. Remember that you can adjust number of hidden layers and number of hidden units in each layer, activation function, etc.\n",
    "* Report the (training) classification accuracy for both.\n",
    "\n",
    "Use tensorflow for coding. This time, you do not have to test the algorithm on test dataset, because the purpose it to understand the importance of representation learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # linear algebra\n",
    "import seaborn as sns\n",
    "sns.set(style='whitegrid')\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "# Begin building the model framework\n",
    "# Declare the variables that need to be learned and initialization\n",
    "# There is one feature, so A's dimension is (2, 1)\n",
    "A = tf.Variable(tf.random_normal(shape = [2,1]))\n",
    "b = tf.Variable(tf.random_normal(shape = [1,1]))\n",
    "init = tf.global_variables_initializer()\n",
    "sess = tf.Session()\n",
    "sess.run(init)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define placeholders\n",
    "data = tf.placeholder(dtype=tf.float32, shape=[None, 2])\n",
    "target = tf.placeholder(dtype=tf.float32, shape=[None, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Declare the model you need to learn\n",
    "mod = tf.matmul(data, A) + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Declare loss function\n",
    "# Use the sigmoid cross-entropy loss function,\n",
    "# first doing a sigmoid on the model result and then using the cross-entropy loss function\n",
    "loss = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(\n",
    "    logits=mod, labels=target))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the learning rate， batch_size etc.\n",
    "learning_rate = 0.005\n",
    "batch_size = 400\n",
    "iter_num = 1500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the optimizer\n",
    "opt = tf.train.GradientDescentOptimizer(learning_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the goal\n",
    "goal = opt.minimize(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the accuracy\n",
    "# The default threshold is 0.5, rounded off directly\n",
    "prediction = tf.round(tf.sigmoid(mod))\n",
    "# Bool into float32 type\n",
    "correct = tf.cast(tf.equal(prediction, target), dtype=tf.float32)\n",
    "# Average\n",
    "accuracy = tf.reduce_mean(correct)\n",
    "# End of the definition of the model framework"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Start training model\n",
    "# Define the variable that stores the result\n",
    "loss_trace = []\n",
    "train_acc = []\n",
    "test_acc = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:  300 loss: 0.731460 accuracy: 0.373500 \n",
      "epoch:  600 loss: 0.721914 accuracy: 0.385500 \n",
      "epoch:  900 loss: 0.705413 accuracy: 0.402500 \n",
      "epoch: 1200 loss: 0.727532 accuracy: 0.414500 \n",
      "epoch: 1500 loss: 0.718238 accuracy: 0.419000 \n"
     ]
    }
   ],
   "source": [
    "\n",
    "# training model\n",
    "for epoch in range(iter_num):\n",
    "    # Generate random batch index\n",
    "    batch_index = np.random.choice(len(X), size=batch_size)\n",
    "    batch_X = X[batch_index]\n",
    "    batch_y = np.matrix(y[batch_index])\n",
    "    sess.run(goal, feed_dict={data: batch_X, target: batch_y})\n",
    "    temp_loss = sess.run(loss, feed_dict={data: batch_X, target: batch_y})\n",
    "    # convert into a matrix, and the shape of the placeholder to correspond\n",
    "    temp_acc = sess.run(accuracy, feed_dict={data: X, target: np.matrix(y)})\n",
    "    # recode the result\n",
    "    loss_trace.append(temp_loss)\n",
    "    train_acc.append(temp_acc)\n",
    "    # output\n",
    "    if (epoch + 1) % 300 == 0:\n",
    "        print('epoch: {:4d} loss: {:5f} accuracy: {:5f} '.format(epoch + 1, temp_loss,temp_acc))\n",
    "        \n",
    "sess.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Feed Forward Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy is  1.0\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "# define computational graph\n",
    "# Create the model\n",
    "x = tf.placeholder(tf.float32, [None, 2])\n",
    "h = tf.layers.dense(x,50)\n",
    "y_m = tf.layers.dense(h,1)\n",
    "\n",
    "#initializer\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "# Define loss and optimizer\n",
    "y_ = tf.placeholder(tf.int64, [None,1])\n",
    "cross_entropy = tf.losses.softmax_cross_entropy(onehot_labels=y_, logits=y_m)\n",
    "train_step = tf.train.GradientDescentOptimizer(0.1).minimize(cross_entropy)\n",
    "\n",
    "loss_log = []\n",
    "batch_size = 100\n",
    "#run the graph as session\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init) # reset values to wrong\n",
    "    # training loop\n",
    "    for _ in range(1000):\n",
    "        batch_index = np.random.choice(len(X), size=batch_size)\n",
    "        batch_xs = X[batch_index]\n",
    "        batch_ys = np.matrix(y[batch_index])\n",
    "        loss,_ = sess.run([cross_entropy,train_step], feed_dict={x: batch_xs, y_: batch_ys})\n",
    "        loss_log.append(loss)\n",
    "\n",
    "    # Test trained model\n",
    "    correct_prediction = tf.equal(tf.argmax(y, 1),tf.argmax(y_,1))\n",
    "    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))\n",
    "    accuracy_result = sess.run(accuracy, feed_dict={x: X,y_: y})\n",
    "    print(\"accuracy is \",accuracy_result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}