Chapter 2.2 神经网络的数据表示.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data representations for neural networks \n",
    "数据存储在多维Numpy数组中，也叫张量(tensor)，它是一个数据容器。  \n",
    "矩阵：二维张；张量的维度(dimension)通常叫做轴(axis)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.1 Scalars (rank-0 tensors)\n",
    "标量 0维张量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array(12)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# int32值类型表示值介于 -2,147,483,648 到 +2,147,483,647 (2^31) 之间的有符号整数 \n",
    "import numpy as np\n",
    "x = np.array(12)\n",
    "print(x.ndim)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.2 Vectors (rank-1 tensors)\n",
    "向量 (1D张量)，只有一个轴"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([12,  3,  6, 14,  7])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([12, 3, 6, 14, 7])\n",
    "print(x.ndim)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这个向量有5个元素，所以被称为5D向量。5D向量不等同于5D张量(亦被称为5阶张量)，后者有5个轴"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.3 Matrices (rank-2 tensors)\n",
    "矩阵(2D张量)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[5, 78, 2, 34, 0],\n",
    "              [6, 79, 3, 35, 1],\n",
    "              [7, 80, 4, 36, 2]])\n",
    "x.ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.4 Rank-3 tensors and higher-rank tensors\n",
    "3D张量与更高维张量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]],\n",
    "              [[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]],\n",
    "              [[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]]])\n",
    "x.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3, 3, 5)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[[[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]],\n",
    "              [[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]],\n",
    "              [[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]]],\n",
    "              [[[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]],\n",
    "              [[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]],\n",
    "              [[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]]]])\n",
    "x.ndim\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.5 Key attributes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "张量的三个关键属性:  \n",
    "   1. 轴的个数(阶段)。3D张量有3个轴，矩阵两个轴，这也叫张量的ndim。  \n",
    "   2. 形状。这是一个整数元祖，表示张量延每个轴的维度大小,这也叫张量的shape。前面4D张量为(2,3,3,5); 3D张量为(3,3,5); 矩阵为(3,5); 向量为(5,); 标量为()。规律为(Xn维度，Xn-1维度,Xn-2维度,...,X1维度)。  \n",
    "   3. 数据类型(dtype)。包括:float32,uint8,float64,char(字符)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow.keras.datasets import mnist\n",
    "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('uint8')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "它是有8位整数组成的3D张量; 6000个28*28的矩阵组成的数组；每个矩阵代表一个灰度图像，元素取值范围为0～255。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Displaying the fourth digit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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 = train_images[4]\n",
    "plt.imshow(digit, cmap=plt.cm.binary)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_labels[4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.6 Manipulating tensors in NumPy\n",
    "在Numpy中操作张量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 28)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images[10].shape #是一个28*28的灰度图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(90, 28, 28)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_slice = train_images[10:100]\n",
    "my_slice.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(90, 28, 28)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_slice = train_images[10:100,:,:] # 等同\n",
    "my_slice.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(90, 28, 28)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_slice = train_images[10:100,0:28,0:28] # 等同，python是从0开始的\n",
    "my_slice.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#在所有图片中，选取14*14的区域\n",
    "my_slice = train_images[:, 14:, 14:]\n",
    "#在所有图片中，在图像中心选取14*14的区域\n",
    "my_slice = train_images[:, 7:-7, 7:-7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.7 The notion of data batches\n",
    "数据批量的概念"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(128, 28, 28)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#深度学习中所有数据张量的第一个轴都是样本轴(sample axis)\n",
    "# 这里将MNIST数据拆成批量为128的小批量\n",
    "batch = train_images[:128]\n",
    "batch.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(128, 28, 28)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batch = train_images[128:256]\n",
    "batch.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 3\n",
    "batch = train_images[128 * n:128 * (n + 1)]\n",
    "# 对于这种批量张量，第一个轴叫做批量轴"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.8 Real-world examples of data tensors¶\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. 向量数据：2D张量, shape = (samples, features) \n",
    "2. 时间序列数据或序列数据: 3D张量, shape = (samples, timesteps, features)  \n",
    "3. 图像: 4D张量, shape = (samples, height, width, channels) or (samples, channels, height, width)  \n",
    "4. 视频: 5D张量, shape = (samples, frames, height, width, channels) or (samples, frames, channels, height, width)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.9 Vector data\n",
    "向量数据：2D张量, shape = (samples, features) \n",
    "第一轴是样本轴，第二个轴是特征轴。  \n",
    "比如  \n",
    "1. 人口统计数据，每个人包括年龄、邮编和收入信息，及三个值的向量。而整个数据集包括100,000个人，因此构成一个(100000,3)的2D张量。  \n",
    "2. 文本数据集，每个文档表示每个单词在其中出现的次数(字典里饱含20,000个常见单词)。每个文档可以被编译成包含20,000个值的向量(每个值对应字典中每个单词的出现次数)，整个数据集包含500个文档，因此可以构成一个(500,20000)的2D张量。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.10 Timeseries data or sequence data  \n",
    "时间序列数据或序列数据: 3D张量, shape = (samples, timesteps, features)\n",
    "一般，把时间轴设置为第二个轴。  \n",
    "1. 股票价格数据集，每一分钟，我们都保存股票的当前价格，前一分钟价格的最高价和最低价，每天共有390分钟，一共保存250天，因此构成一个(250,390,3)的3D张量。  \n",
    "2. 推文数据集，每条推文编译成280个字符组成的序列，每个字符又来自128个字符组成的字幕表，100万条推文可构成(1000000,280,128)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.11 Image data\n",
    "图像: 4D张量, shape =   \n",
    "(samples, height, width, channels) --TensorFlow  \n",
    "or  \n",
    "(samples, channels, height, width) --Theano  \n",
    "图像通常具有三个维度: 高/宽/颜色深度。  \n",
    "128张图像大小为256*256的灰度图像构成 (128,256,256,1)的张量。  \n",
    "128张彩色图像构成 (128,256,256,3)的张量。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.12 Video data\n",
    "视频: 5D张量, shape = (samples, frames, height, width, channels) or (samples, frames, channels, height, width)  \n",
    "一个每秒4帧，尺寸为144*256的60s彩色视频可构成 (4,240,144,256,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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