柏穎0523.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "env: KERAS_BACKEND=tensorflow\n"
     ]
    }
   ],
   "source": [
    "%env KERAS_BACKEND=tensorflow\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from ipywidgets import interact, FloatSlider"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/wuyouxin/anaconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "# Keras functions\n",
    "from keras.models import Sequential, Model\n",
    "from keras.layers import Input, Lambda, concatenate\n",
    "from keras.layers import Dense\n",
    "from keras.layers import Conv2D, MaxPooling2D\n",
    "from keras.layers import Conv2DTranspose, UpSampling2D\n",
    "from keras.optimizers import SGD, Adam\n",
    "from keras import metrics\n",
    "\n",
    "# Keras dataset\n",
    "from keras.datasets import mnist\n",
    "\n",
    "# Keras utilis function\n",
    "from keras.utils import np_utils\n",
    "\n",
    "from keras import backend as K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train0, y_train0), (x_test0, y_test0) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = x_train0.reshape(60000, -1)\n",
    "x_test = x_test0.reshape(10000, -1)\n",
    "\n",
    "x_train -= x_train.min()\n",
    "x_train = x_train/x_train.max()\n",
    "enc_1 = Dense(100, activation='sigmoid')\n",
    "enc_mean = Dense(2) \n",
    "enc_log_var = Dense(2)  \n",
    "\n",
    "dec_2 = Dense(100, activation='sigmoid')\n",
    "dec_1 = Dense(784, activation='sigmoid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Input(shape=(784,))\n",
    "enc_x = enc_1(x)\n",
    "\n",
    "z_mean = enc_mean(enc_x)\n",
    "z_log_var = enc_log_var(enc_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sampling(args):\n",
    "    z_mean, z_log_var = args\n",
    "    epsilon = K.random_normal(shape=(2,), mean=0., stddev=1)\n",
    "    return z_mean + K.exp(z_log_var / 2) * epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "input_1 (InputLayer)            (None, 784)          0                                            \n",
      "__________________________________________________________________________________________________\n",
      "dense_1 (Dense)                 (None, 100)          78500       input_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_2 (Dense)                 (None, 2)            202         dense_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_3 (Dense)                 (None, 2)            202         dense_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "lambda_1 (Lambda)               (None, 2)            0           dense_2[0][0]                    \n",
      "                                                                 dense_3[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_4 (Dense)                 (None, 100)          300         lambda_1[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "dense_5 (Dense)                 (None, 784)          79184       dense_4[0][0]                    \n",
      "==================================================================================================\n",
      "Total params: 158,388\n",
      "Trainable params: 158,388\n",
      "Non-trainable params: 0\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "z = Lambda(sampling, output_shape=(2,))([z_mean, z_log_var])\n",
    "dec_x = dec_2(z)\n",
    "x_hat = dec_1(dec_x)\n",
    "VAE = Model(x, x_hat)\n",
    "VAE.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vae_loss(x, x_recon):  \n",
    "    recovery_loss = 784 * metrics.binary_crossentropy(x, x_recon)\n",
    "    kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)\n",
    "    return recovery_loss + kl_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_1 (InputLayer)         (None, 784)               0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 100)               78500     \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 2)                 202       \n",
      "=================================================================\n",
      "Total params: 78,702\n",
      "Trainable params: 78,702\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "VAE.compile(loss=vae_loss, optimizer=Adam())\n",
    "VAE.load_weights('VAE_handwriting_model_weights.h5')\n",
    "VAE_Encoder = Model(x, z_mean)\n",
    "\n",
    "VAE_Encoder.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_2 (InputLayer)         (None, 2)                 0         \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 100)               300       \n",
      "_________________________________________________________________\n",
      "dense_5 (Dense)              (None, 784)               79184     \n",
      "=================================================================\n",
      "Total params: 79,484\n",
      "Trainable params: 79,484\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "h_input = Input(shape=(2,))\n",
    "VAE_Decoder = Model(h_input, dec_1(dec_2(h_input)))\n",
    "\n",
    "VAE_Decoder.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第 1255 圖的 latent 表示為 [[-0.6285221 -1.0816461]]\n"
     ]
    }
   ],
   "source": [
    "idx = np.random.randint(x_train.shape[0])\n",
    "print(\"第 %d 圖的 latent 表示為 %s\" %(idx, VAE_Encoder.predict(x_train[idx: idx+1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "indices = np.random.randint(x_test.shape[0], size=2000)\n",
    "VAE_latents = VAE_Encoder.predict(x_test[indices])\n",
    "plt.scatter(VAE_latents[:, 0], VAE_latents[:, 1], c=y_test0[indices], cmap='tab20')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalized(x):\n",
    "    x -= x.min()\n",
    "    x /= x.max()\n",
    "    return x\n",
    "n=10\n",
    "digit_size = 28\n",
    "\n",
    "grid_x_vae = np.linspace(-4+0.05, 4-0.05, n)\n",
    "grid_y_vae = np.linspace(4+0.05, 4-0.05, n)\n",
    "VAE_figure = np.zeros((digit_size * n, digit_size * n))\n",
    "for i, yi in enumerate(grid_x_vae):\n",
    "    for j, xi in enumerate(grid_y_vae):\n",
    "\n",
    "        z_sample = np.array([[xi, yi]])\n",
    "        x_decoded = VAE_Decoder.predict(z_sample)\n",
    "        digit = x_decoded[0].reshape(digit_size, digit_size)\n",
    "        VAE_figure[(n-i-1) * digit_size: (n - i) * digit_size,\n",
    "                   j * digit_size: (j + 1) * digit_size] = normalized(digit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 15))\n",
    "plt.imshow(VAE_figure, cmap='Greys')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inBetween(t):\n",
    "    data_0 = x_train0[idx_1]\n",
    "    data_1 = x_train0[idx_2]\n",
    "    data_t = (1-t)*x_train0[idx_1] + t*x_train0[idx_2]\n",
    "\n",
    "    mu_0 = VAE_Encoder.predict(x_train[idx_1:idx_1+1]).squeeze()\n",
    "    mu_1 = VAE_Encoder.predict(x_train[idx_2:idx_2+1]).squeeze()\n",
    "    mu_t = (1-t)*mu_0 + t*mu_1\n",
    "\n",
    "    plt.figure(figsize=(10, 5))\n",
    "    ax1 = plt.subplot(2, 1, 2)\n",
    "    ax1.scatter(mu_0[0], mu_0[1])\n",
    "    ax1.scatter(mu_1[0], mu_1[1])\n",
    "    ax1.scatter(mu_t[0], mu_t[1])\n",
    "\n",
    "    ax2 = plt.subplot(2, 3, 1)\n",
    "    ax2.imshow(data_0, cmap='Greys')\n",
    "\n",
    "    ax3 = plt.subplot(2, 3, 2)\n",
    "    ax3.imshow(data_t, cmap='Greys')\n",
    "\n",
    "    ax4 = plt.subplot(2, 3, 3)\n",
    "    ax4.imshow(data_1, cmap='Greys')\n",
    "idx_1, idx_2 = np.random.randint(x_test.shape[0], size=2)\n",
    "data_0 = x_train0[idx_1]\n",
    "data_1 = x_train0[idx_2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6f794bbd6e7045ebb5152606146d31af",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description='t', max=1.0, step=0.05), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.inBetween(t)>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interact(inBetween, t=FloatSlider(value=0.5, \n",
    "                                  min=0, \n",
    "                                  max=1.0,\n",
    "                                  step=0.05,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}