keras mnsit.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading data from https://s3.amazonaws.com/img-datasets/mnist.npz\n",
      "11493376/11490434 [==============================] - 55s 5us/step\n",
      "11501568/11490434 [==============================] - 55s 5us/step\n"
     ]
    }
   ],
   "source": [
    "from keras.datasets import mnist\n",
    "\n",
    "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "60000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(train_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 28, 28)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(test_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras import models\n",
    "from keras import layers\n",
    "\n",
    "network = models.Sequential()\n",
    "network.add(layers.Dense(512, activation='relu', input_shape=(28 * 28,)))\n",
    "network.add(layers.Dense(10, activation='softmax'))\n",
    "network.compile(optimizer='rmsprop',\n",
    "                loss='categorical_crossentropy',\n",
    "                metrics=['accuracy'])\n",
    "\n",
    "train_images = train_images.reshape((60000, 28 * 28))\n",
    "train_images = train_images.astype('float32') / 255\n",
    "test_images = test_images.reshape((10000, 28 * 28))\n",
    "test_images = test_images.astype('float32') / 255"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/5\n",
      "60000/60000 [==============================] - 4s 71us/step - loss: 0.2541 - acc: 0.9266\n",
      "Epoch 2/5\n",
      "60000/60000 [==============================] - 4s 69us/step - loss: 0.1028 - acc: 0.9694\n",
      "Epoch 3/5\n",
      "60000/60000 [==============================] - 4s 69us/step - loss: 0.0678 - acc: 0.9795\n",
      "Epoch 4/5\n",
      "60000/60000 [==============================] - 4s 69us/step - loss: 0.0493 - acc: 0.9851\n",
      "Epoch 5/5\n",
      "60000/60000 [==============================] - 4s 69us/step - loss: 0.0372 - acc: 0.9890\n",
      "10000/10000 [==============================] - 1s 51us/step\n"
     ]
    }
   ],
   "source": [
    "from keras.utils import to_categorical\n",
    "train_labels = to_categorical(train_labels)\n",
    "test_labels = to_categorical(test_labels)\n",
    "\n",
    "network.fit(train_images, train_labels, epochs=5, batch_size=128)\n",
    "\n",
    "test_loss, test_acc = network.evaluate(test_images, test_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07221246116398834 0.9785\n"
     ]
    }
   ],
   "source": [
    "print test_loss, test_acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "digit = train_images[4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "digit = digit.reshape(28,28)\n",
    "plt.imshow(digit, cmap=plt.cm.binary)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Error when checking input: expected dense_1_input to have shape (784,) but got array with shape (1,)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-23-07d3ff6623c6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mnetwork\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdigit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m28\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m28\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/home/wolf/anaconda2/lib/python2.7/site-packages/keras/engine/training.pyc\u001b[0m in \u001b[0;36mpredict\u001b[0;34m(self, x, batch_size, verbose, steps)\u001b[0m\n\u001b[1;32m   1147\u001b[0m                              'argument.')\n\u001b[1;32m   1148\u001b[0m         \u001b[0;31m# Validate user data.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1149\u001b[0;31m         \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_standardize_user_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1150\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstateful\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1151\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0mbatch_size\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mbatch_size\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/wolf/anaconda2/lib/python2.7/site-packages/keras/engine/training.pyc\u001b[0m in \u001b[0;36m_standardize_user_data\u001b[0;34m(self, x, y, sample_weight, class_weight, check_array_lengths, batch_size)\u001b[0m\n\u001b[1;32m    749\u001b[0m             \u001b[0mfeed_input_shapes\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    750\u001b[0m             \u001b[0mcheck_batch_axis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0;31m# Don't enforce the batch size.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 751\u001b[0;31m             exception_prefix='input')\n\u001b[0m\u001b[1;32m    752\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    753\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/wolf/anaconda2/lib/python2.7/site-packages/keras/engine/training_utils.pyc\u001b[0m in \u001b[0;36mstandardize_input_data\u001b[0;34m(data, names, shapes, check_batch_axis, exception_prefix)\u001b[0m\n\u001b[1;32m    136\u001b[0m                             \u001b[0;34m': expected '\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnames\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m' to have shape '\u001b[0m \u001b[0;34m+\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    137\u001b[0m                             \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m' but got array with shape '\u001b[0m \u001b[0;34m+\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 138\u001b[0;31m                             str(data_shape))\n\u001b[0m\u001b[1;32m    139\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    140\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Error when checking input: expected dense_1_input to have shape (784,) but got array with shape (1,)"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "network.predict(np.array(digit.reshape(28*28)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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