03-TF-Neural-Network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# First Neurons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Set Random Seeds for same results **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(101)\n",
    "tf.set_random_seed(101)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Data Setup **"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setting Up some Random Data for Demonstration Purposes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 51.63986277,  57.06675869,   2.84742265,  17.15216562,\n",
       "         68.52769817],\n",
       "       [ 83.38968626,  30.69662197,  89.36130797,  72.15438618,\n",
       "         18.99389542],\n",
       "       [ 55.42275911,  35.2131954 ,  18.18924027,  78.56017619,\n",
       "         96.54832224],\n",
       "       [ 23.23536618,   8.35614337,  60.35484223,  72.89927573,\n",
       "         27.62388285],\n",
       "       [ 68.53063288,  51.78674742,   4.84845374,  13.78692376,\n",
       "         18.69674261]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand_a = np.random.uniform(0,100,(5,5))\n",
    "rand_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 99.43179012],\n",
       "       [ 52.06653967],\n",
       "       [ 57.87895355],\n",
       "       [ 73.48190583],\n",
       "       [ 54.19617722]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand_b = np.random.uniform(0,100,(5,1))\n",
    "rand_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# CONFIRM SAME  RANDOM NUMBERS (EXECUTE SEED IN SAME CELL!) Watch video for explanation\n",
    "np.random.seed(101)\n",
    "rand_a = np.random.uniform(0,100,(5,5))\n",
    "rand_b = np.random.uniform(0,100,(5,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Placeholders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = tf.placeholder(tf.float32)\n",
    "b = tf.placeholder(tf.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "add_op = a+b # tf.add(a,b)\n",
    "mult_op = a*b #tf.multiply(a,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Running Sessions  to create Graphs with Feed Dictionaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 151.07165527  156.49855042  102.27921295  116.58396149  167.95948792]\n",
      " [ 135.45622253   82.76316071  141.42784119  124.22093201   71.06043243]\n",
      " [ 113.30171204   93.09214783   76.06819153  136.43911743  154.42727661]\n",
      " [  96.7172699    81.83804321  133.83674622  146.38117981  101.10578918]\n",
      " [ 122.72680664  105.98292542   59.04463196   67.98310089   72.89292145]]\n",
      "\n",
      "\n",
      "[[ 5134.64404297  5674.25         283.12432861  1705.47070312\n",
      "   6813.83154297]\n",
      " [ 4341.8125      1598.26696777  4652.73388672  3756.8293457    988.9463501 ]\n",
      " [ 3207.8112793   2038.10290527  1052.77416992  4546.98046875\n",
      "   5588.11572266]\n",
      " [ 1707.37902832   614.02526855  4434.98876953  5356.77734375\n",
      "   2029.85546875]\n",
      " [ 3714.09838867  2806.64379883   262.76763916   747.19854736\n",
      "   1013.29199219]]\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    add_result = sess.run(add_op,feed_dict={a:rand_a,b:rand_b})\n",
    "    print(add_result)\n",
    "    \n",
    "    print('\\n')\n",
    "    \n",
    "    mult_result = sess.run(mult_op,feed_dict={a:rand_a,b:rand_b})\n",
    "    print(mult_result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "________________________\n",
    "\n",
    "________________________"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_features = 10\n",
    "n_dense_neurons = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Placeholder for x\n",
    "x = tf.placeholder(tf.float32,(None,n_features))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Variables for w and b\n",
    "b = tf.Variable(tf.zeros([n_dense_neurons]))\n",
    "\n",
    "W = tf.Variable(tf.random_normal([n_features,n_dense_neurons]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Operation Activation Function **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xW = tf.matmul(x,W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z = tf.add(xW,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# tf.nn.relu() or tf.tanh()\n",
    "a = tf.sigmoid(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Variable Intializer! **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "    \n",
    "    layer_out = sess.run(a,feed_dict={x : np.random.random([1,n_features])})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.63504547  0.48962751  0.98692095]]\n"
     ]
    }
   ],
   "source": [
    "print(layer_out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We still need to finish off this process with optimization! Let's learn how to do this next.\n",
    "\n",
    "_____"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Full Network Example\n",
    "\n",
    "Let's work on a regression example, we are trying to solve a very simple equation:\n",
    "\n",
    "y = mx + b\n",
    "\n",
    "y will be the y_labels and x is the x_data. We are trying to figure out the slope and the intercept for the line that best fits our data!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Artifical Data (Some Made Up Regression Data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_data = np.linspace(0,10,10) + np.random.uniform(-1.5,1.5,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.23946067,  2.03487156,  1.93121571,  2.90500636,  5.80307459,\n",
       "        5.08645029,  7.76196612,  8.76861091,  9.00337324, 11.26740812])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_label = np.linspace(0,10,10) + np.random.uniform(-1.5,1.5,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f053c7ccdd0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aq8ZKUQBIYtB76ACQBoEOAEkQ6ACQBIEOAEkQ6ACQBIEOAEkQ6ACQBIEOAEn8Hxx2a5R99n9eAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_data,y_label,'*')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Variables **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.39470907,  0.20018792])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = tf.Variable(0.39)\n",
    "b = tf.Variable(0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cost Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "error = 0\n",
    "\n",
    "for x,y in zip(x_data,y_label):\n",
    "    \n",
    "    y_hat = m*x + b  #Our predicted value\n",
    "    \n",
    "    error += (y-y_hat)**2 # The cost we want to minimize (we'll need to use an optimization function for the minimization!)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.001)\n",
    "train = optimizer.minimize(error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialize Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Session and Run!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "with tf.Session() as sess:\n",
    "    \n",
    "    sess.run(init)\n",
    "    \n",
    "    epochs = 1000\n",
    "    \n",
    "    for i in range(epochs):\n",
    "        \n",
    "        sess.run(train)\n",
    "        \n",
    "\n",
    "    # Fetch Back Results\n",
    "    final_slope , final_intercept = sess.run([m,b])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97030795"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.637274"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluate Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f053c23d650>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "x_test = np.linspace(-1,11,10)\n",
    "y_pred_plot = final_slope*x_test + final_intercept\n",
    "\n",
    "plt.plot(x_test,y_pred_plot,'b')\n",
    "\n",
    "plt.plot(x_data,y_label,'*')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Great Job!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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