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618 行
20 KiB
618 行
20 KiB
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"from google.colab import drive\n",
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"\n",
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"drive.mount('/content/drive', force_remount=True)\n",
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"\n",
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"# 输入daseCV所在的路径\n",
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"# 'daseCV' 文件夹包括 '.py', 'classifiers' 和'datasets'文件夹\n",
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"# 例如 'CV/assignments/assignment1/daseCV/'\n",
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"FOLDERNAME = None\n",
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"\n",
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"assert FOLDERNAME is not None, \"[!] Enter the foldername.\"\n",
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"\n",
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"%cd drive/My\\ Drive\n",
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"%cp -r $FOLDERNAME ../../\n",
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"%cd ../../\n",
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"%cd daseCV/datasets/\n",
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"!bash get_datasets.sh\n",
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"%cd ../../"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"tags": [
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"pdf-title"
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]
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},
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"source": [
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"# 多分类支撑向量机练习\n",
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"*完成此练习并且上交本ipynb（包含输出及代码）.*\n",
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"\n",
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"在这个练习中，你将会:\n",
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" \n",
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"- 为SVM构建一个完全向量化的**损失函数**\n",
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"- 实现**解析梯度**的向量化表达式\n",
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"- 使用数值梯度检查你的代码是否正确\n",
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"- 使用验证集**调整学习率和正则化项**\n",
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"- 用**SGD（随机梯度下降）** **优化**损失函数\n",
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"- **可视化** 最后学习到的权重\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"tags": [
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"pdf-ignore"
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]
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},
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"outputs": [],
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"source": [
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"# 导入包\n",
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"import random\n",
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"import numpy as np\n",
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"from daseCV.data_utils import load_CIFAR10\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"# 下面一行是notebook的magic命令，作用是让matplotlib在notebook内绘图（而不是新建一个窗口）\n",
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"%matplotlib inline\n",
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"plt.rcParams['figure.figsize'] = (10.0, 8.0) # 设置绘图的默认大小\n",
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"plt.rcParams['image.interpolation'] = 'nearest'\n",
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"plt.rcParams['image.cmap'] = 'gray'\n",
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"\n",
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"# 该magic命令可以重载外部的python模块\n",
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"# 相关资料可以去看 http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython\n",
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"%load_ext autoreload\n",
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"%autoreload 2"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"tags": [
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"pdf-ignore"
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]
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},
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"source": [
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"## 准备和预处理CIFAR-10的数据"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"tags": [
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"pdf-ignore"
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]
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},
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"outputs": [],
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"source": [
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"# 导入原始CIFAR-10数据\n",
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"cifar10_dir = 'daseCV/datasets/cifar-10-batches-py'\n",
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"\n",
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"# 清空变量，防止多次定义变量（可能造成内存问题）\n",
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"try:\n",
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" del X_train, y_train\n",
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" del X_test, y_test\n",
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" print('Clear previously loaded data.')\n",
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"except:\n",
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" pass\n",
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"\n",
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"X_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)\n",
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"\n",
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"# 完整性检查，打印出训练和测试数据的大小\n",
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"print('Training data shape: ', X_train.shape)\n",
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"print('Training labels shape: ', y_train.shape)\n",
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"print('Test data shape: ', X_test.shape)\n",
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"print('Test labels shape: ', y_test.shape)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"tags": [
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"pdf-ignore"
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]
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},
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"outputs": [],
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"source": [
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"# 可视化部分数据\n",
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"# 这里我们每个类别展示了7张图片\n",
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"classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']\n",
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"num_classes = len(classes)\n",
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"samples_per_class = 7\n",
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"for y, cls in enumerate(classes):\n",
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" idxs = np.flatnonzero(y_train == y)\n",
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" idxs = np.random.choice(idxs, samples_per_class, replace=False)\n",
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" for i, idx in enumerate(idxs):\n",
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" plt_idx = i * num_classes + y + 1\n",
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" plt.subplot(samples_per_class, num_classes, plt_idx)\n",
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" plt.imshow(X_train[idx].astype('uint8'))\n",
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" plt.axis('off')\n",
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" if i == 0:\n",
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" plt.title(cls)\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"tags": [
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"pdf-ignore"
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]
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},
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"outputs": [],
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"source": [
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"# 划分训练集，验证集和测试集，除此之外，\n",
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"# 我们从训练集中抽取了一小部分作为代码开发的数据，\n",
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"# 使用小批量的开发数据集能够快速开发代码\n",
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"num_training = 49000\n",
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"num_validation = 1000\n",
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"num_test = 1000\n",
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"num_dev = 500\n",
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"\n",
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"# 从原始训练集中抽取出num_validation个样本作为验证集\n",
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"mask = range(num_training, num_training + num_validation)\n",
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"X_val = X_train[mask]\n",
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"y_val = y_train[mask]\n",
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"\n",
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"# 从原始训练集中抽取出num_training个样本作为训练集\n",
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"mask = range(num_training)\n",
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"X_train = X_train[mask]\n",
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"y_train = y_train[mask]\n",
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"\n",
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"# 从训练集中抽取num_dev个样本作为开发数据集\n",
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"mask = np.random.choice(num_training, num_dev, replace=False)\n",
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"X_dev = X_train[mask]\n",
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"y_dev = y_train[mask]\n",
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"\n",
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"# 从原始测试集中抽取num_test个样本作为测试集\n",
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"mask = range(num_test)\n",
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"X_test = X_test[mask]\n",
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"y_test = y_test[mask]\n",
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"\n",
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"print('Train data shape: ', X_train.shape)\n",
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"print('Train labels shape: ', y_train.shape)\n",
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"print('Validation data shape: ', X_val.shape)\n",
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"print('Validation labels shape: ', y_val.shape)\n",
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"print('Test data shape: ', X_test.shape)\n",
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"print('Test labels shape: ', y_test.shape)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"tags": [
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"pdf-ignore"
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]
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},
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"outputs": [],
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"source": [
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"# 预处理：把图片数据rehspae成行向量\n",
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"X_train = np.reshape(X_train, (X_train.shape[0], -1))\n",
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"X_val = np.reshape(X_val, (X_val.shape[0], -1))\n",
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"X_test = np.reshape(X_test, (X_test.shape[0], -1))\n",
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"X_dev = np.reshape(X_dev, (X_dev.shape[0], -1))\n",
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"\n",
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"# 完整性检查，打印出数据的shape\n",
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"print('Training data shape: ', X_train.shape)\n",
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"print('Validation data shape: ', X_val.shape)\n",
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"print('Test data shape: ', X_test.shape)\n",
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"print('dev data shape: ', X_dev.shape)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"tags": [
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"pdf-ignore-input"
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]
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},
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"outputs": [],
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"source": [
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"# 预处理：减去image的平均值（均值规整化）\n",
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"# 第一步：计算训练集中的图像均值\n",
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"mean_image = np.mean(X_train, axis=0)\n",
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"print(mean_image[:10]) # print a few of the elements\n",
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"plt.figure(figsize=(4,4))\n",
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"plt.imshow(mean_image.reshape((32,32,3)).astype('uint8')) # visualize the mean image\n",
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"plt.show()\n",
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"\n",
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"# 第二步：所有数据集减去均值\n",
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"X_train -= mean_image\n",
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"X_val -= mean_image\n",
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"X_test -= mean_image\n",
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"X_dev -= mean_image\n",
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"\n",
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"# 第三步：拼接一个bias维，其中所有值都是1（bias trick），\n",
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"# SVM可以联合优化数据和bias，即只需要优化一个权值矩阵W\n",
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"X_train = np.hstack([X_train, np.ones((X_train.shape[0], 1))])\n",
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"X_val = np.hstack([X_val, np.ones((X_val.shape[0], 1))])\n",
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"X_test = np.hstack([X_test, np.ones((X_test.shape[0], 1))])\n",
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"X_dev = np.hstack([X_dev, np.ones((X_dev.shape[0], 1))])\n",
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"\n",
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"print(X_train.shape, X_val.shape, X_test.shape, X_dev.shape)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## SVM分类器\n",
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"\n",
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"你需要在**daseCV/classifiers/linear_svm.py**里面完成编码\n",
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"\n",
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"我们已经预先定义了一个函数`compute_loss_naive`，该函数使用循环来计算多分类SVM损失函数"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 调用朴素版的损失计算函数\n",
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"from daseCV.classifiers.linear_svm import svm_loss_naive\n",
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"import time\n",
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"\n",
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"# 生成一个随机的SVM权值矩阵（矩阵值很小）\n",
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"W = np.random.randn(3073, 10) * 0.0001 \n",
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"\n",
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"loss, grad = svm_loss_naive(W, X_dev, y_dev, 0.000005)\n",
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"print('loss: %f' % (loss, ))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"从上面的函数返回的`grad`现在是零。请推导支持向量机损失函数的梯度，并在svm_loss_naive中编码实现。\n",
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"\n",
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"为了检查是否正确地实现了梯度，你可以用数值方法估计损失函数的梯度，并将数值估计与你计算出来的梯度进行比较。我们已经为你提供了检查的代码:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 一旦你实现了梯度计算的功能，重新执行下面的代码检查梯度\n",
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"\n",
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"# 计算损失和W的梯度\n",
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"loss, grad = svm_loss_naive(W, X_dev, y_dev, 0.0)\n",
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"\n",
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"# 数值估计梯度的方法沿着随机几个维度进行计算，并且和解析梯度进行比较，\n",
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"# 这两个方法算出来的梯度应该在任何维度上完全一致(相对误差足够小)\n",
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"from daseCV.gradient_check import grad_check_sparse\n",
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"f = lambda w: svm_loss_naive(w, X_dev, y_dev, 0.0)[0]\n",
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"grad_numerical = grad_check_sparse(f, W, grad)\n",
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"\n",
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"# 把正则化项打开后继续再检查一遍梯度\n",
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"# 你没有忘记正则化项吧？（忘了的罚抄100遍(๑•́ ₃•̀๑) ）\n",
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"loss, grad = svm_loss_naive(W, X_dev, y_dev, 5e1)\n",
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"f = lambda w: svm_loss_naive(w, X_dev, y_dev, 5e1)[0]\n",
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"grad_numerical = grad_check_sparse(f, W, grad)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"tags": [
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"pdf-inline"
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]
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},
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"source": [
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"**问题 1**\n",
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"\n",
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"有可能会出现某一个维度上的gradcheck没有完全匹配。这个问题是怎么引起的？有必要担心这个问题么？请举一个简单例子，能够导致梯度检查失败。如何改进这个问题？*提示：SVM的损失函数不是严格可微的*\n",
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"\n",
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"$\\color{blue}{ 你的回答：}$ *在这里填写* \n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 接下来实现svm_loss_vectorized函数，目前只计算损失\n",
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"# 稍后再计算梯度\n",
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"tic = time.time()\n",
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"loss_naive, grad_naive = svm_loss_naive(W, X_dev, y_dev, 0.000005)\n",
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"toc = time.time()\n",
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"print('Naive loss: %e computed in %fs' % (loss_naive, toc - tic))\n",
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"\n",
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"from daseCV.classifiers.linear_svm import svm_loss_vectorized\n",
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"tic = time.time()\n",
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"loss_vectorized, _ = svm_loss_vectorized(W, X_dev, y_dev, 0.000005)\n",
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"toc = time.time()\n",
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"print('Vectorized loss: %e computed in %fs' % (loss_vectorized, toc - tic))\n",
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"\n",
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"# 两种方法算出来的损失应该是相同的，但是向量化实现的方法应该更快\n",
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"print('difference: %f' % (loss_naive - loss_vectorized))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 完成svm_loss_vectorized函数，并用向量化方法计算梯度\n",
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"\n",
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"# 朴素方法和向量化实现的梯度应该相同，但是向量化方法也应该更快\n",
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"tic = time.time()\n",
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"_, grad_naive = svm_loss_naive(W, X_dev, y_dev, 0.000005)\n",
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"toc = time.time()\n",
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"print('Naive loss and gradient: computed in %fs' % (toc - tic))\n",
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"\n",
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"tic = time.time()\n",
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"_, grad_vectorized = svm_loss_vectorized(W, X_dev, y_dev, 0.000005)\n",
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"toc = time.time()\n",
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"print('Vectorized loss and gradient: computed in %fs' % (toc - tic))\n",
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"\n",
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"# 损失是一个标量，因此很容易比较两种方法算出的值，\n",
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"# 而梯度是一个矩阵，所以我们用Frobenius范数来比较梯度的值\n",
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"difference = np.linalg.norm(grad_naive - grad_vectorized, ord='fro')\n",
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"print('difference: %f' % difference)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 随机梯度下降（Stochastic Gradient Descent）\n",
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"\n",
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"我们现在有了向量化的损失函数表达式和梯度表达式，同时我们计算的梯度和数值梯度是匹配的。\n",
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"接下来我们要做SGD。"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 在linear_classifier.py文件中，编码实现LinearClassifier.train()中的SGD功能，\n",
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"# 运行下面的代码\n",
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"from daseCV.classifiers import LinearSVM\n",
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"svm = LinearSVM()\n",
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"tic = time.time()\n",
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"loss_hist = svm.train(X_train, y_train, learning_rate=1e-7, reg=2.5e4,\n",
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" num_iters=1500, verbose=True)\n",
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"toc = time.time()\n",
|
|
"print('That took %fs' % (toc - tic))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# 一个有用的debugging技巧是把损失函数画出来\n",
|
|
"plt.plot(loss_hist)\n",
|
|
"plt.xlabel('Iteration number')\n",
|
|
"plt.ylabel('Loss value')\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# 完成LinearSVM.predict函数,并且在训练集和验证集上评估其准确性\n",
|
|
"y_train_pred = svm.predict(X_train)\n",
|
|
"print('training accuracy: %f' % (np.mean(y_train == y_train_pred), ))\n",
|
|
"y_val_pred = svm.predict(X_val)\n",
|
|
"print('validation accuracy: %f' % (np.mean(y_val == y_val_pred), ))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"tags": [
|
|
"code"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# 使用验证集来调整超参数(正则化强度和学习率)。\n",
|
|
"# 你可以尝试不同的学习速率和正则化项的值;\n",
|
|
"# 如果你细心的话,您应该可以在验证集上获得大约0.39的准确率。\n",
|
|
"\n",
|
|
"# 注意:在搜索超参数时，您可能会看到runtime/overflow的警告。\n",
|
|
"# 这是由极端超参值造成的,不是代码的bug。\n",
|
|
"\n",
|
|
"learning_rates = [1e-7, 5e-5]\n",
|
|
"regularization_strengths = [2.5e4, 5e4]\n",
|
|
"\n",
|
|
"# results是一个字典,把元组(learning_rate, regularization_strength)映射到元组(training_accuracy, validation_accuracy) \n",
|
|
"# accuracy是样本中正确分类的比例\n",
|
|
"results = {}\n",
|
|
"best_val = -1 # 我们迄今为止见过最好的验证集准确率\n",
|
|
"best_svm = None # 拥有最高验证集准确率的LinearSVM对象\n",
|
|
"\n",
|
|
"##############################################################################\n",
|
|
"# TODO：\n",
|
|
"# 编写代码，通过比较验证集的准确度来选择最佳超参数。\n",
|
|
"# 对于每个超参数组合，在训练集上训练一个线性SVM，在训练集和验证集上计算它的精度，\n",
|
|
"# 并将精度结果存储在results字典中。此外，在best_val中存储最高验证集准确度，\n",
|
|
"# 在best_svm中存储拥有此精度的SVM对象。\n",
|
|
"#\n",
|
|
"# 提示: \n",
|
|
"# 在开发代码时，应该使用一个比较小的num_iter值，这样SVM就不会花费太多时间训练; \n",
|
|
"# 一旦您确信您的代码开发完成，您就应该使用一个较大的num_iter值重新训练并验证。\n",
|
|
"##############################################################################\n",
|
|
"# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****\n",
|
|
"\n",
|
|
"pass\n",
|
|
" \n",
|
|
"# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****\n",
|
|
" \n",
|
|
"# 打印results\n",
|
|
"for lr, reg in sorted(results):\n",
|
|
" train_accuracy, val_accuracy = results[(lr, reg)]\n",
|
|
" print('lr %e reg %e train accuracy: %f val accuracy: %f' % (\n",
|
|
" lr, reg, train_accuracy, val_accuracy))\n",
|
|
" \n",
|
|
"print('best validation accuracy achieved during cross-validation: %f' % best_val)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"tags": [
|
|
"pdf-ignore-input"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# 可是化交叉验证结果\n",
|
|
"import math\n",
|
|
"x_scatter = [math.log10(x[0]) for x in results]\n",
|
|
"y_scatter = [math.log10(x[1]) for x in results]\n",
|
|
"\n",
|
|
"# 画出训练集准确率\n",
|
|
"marker_size = 100\n",
|
|
"colors = [results[x][0] for x in results]\n",
|
|
"plt.subplot(2, 1, 1)\n",
|
|
"plt.scatter(x_scatter, y_scatter, marker_size, c=colors, cmap=plt.cm.coolwarm)\n",
|
|
"plt.colorbar()\n",
|
|
"plt.xlabel('log learning rate')\n",
|
|
"plt.ylabel('log regularization strength')\n",
|
|
"plt.title('CIFAR-10 training accuracy')\n",
|
|
"\n",
|
|
"# 画出验证集准确率\n",
|
|
"colors = [results[x][1] for x in results] # default size of markers is 20\n",
|
|
"plt.subplot(2, 1, 2)\n",
|
|
"plt.scatter(x_scatter, y_scatter, marker_size, c=colors, cmap=plt.cm.coolwarm)\n",
|
|
"plt.colorbar()\n",
|
|
"plt.xlabel('log learning rate')\n",
|
|
"plt.ylabel('log regularization strength')\n",
|
|
"plt.title('CIFAR-10 validation accuracy')\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# 在测试集上测试最好的SVM分类器\n",
|
|
"y_test_pred = best_svm.predict(X_test)\n",
|
|
"test_accuracy = np.mean(y_test == y_test_pred)\n",
|
|
"print('linear SVM on raw pixels final test set accuracy: %f' % test_accuracy)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"tags": [
|
|
"pdf-ignore-input"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# 画出每一类的权重\n",
|
|
"# 基于您选择的学习速度和正则化强度，画出来的可能不好看\n",
|
|
"w = best_svm.W[:-1,:] # 去掉bias\n",
|
|
"w = w.reshape(32, 32, 3, 10)\n",
|
|
"w_min, w_max = np.min(w), np.max(w)\n",
|
|
"classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']\n",
|
|
"for i in range(10):\n",
|
|
" plt.subplot(2, 5, i + 1)\n",
|
|
" \n",
|
|
" # 将权重调整为0到255之间\n",
|
|
" wimg = 255.0 * (w[:, :, :, i].squeeze() - w_min) / (w_max - w_min)\n",
|
|
" plt.imshow(wimg.astype('uint8'))\n",
|
|
" plt.axis('off')\n",
|
|
" plt.title(classes[i])"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"tags": [
|
|
"pdf-inline"
|
|
]
|
|
},
|
|
"source": [
|
|
"**问题2**\n",
|
|
"\n",
|
|
"描述你的可视化权值是什么样子的，并提供一个简短的解释为什么它们看起来是这样的。\n",
|
|
"\n",
|
|
"$\\color{blue}{ 你的回答： }$ *请在这里填写* \n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"---\n",
|
|
"# 重要\n",
|
|
"\n",
|
|
"这里是作业的结尾处，请执行以下步骤:\n",
|
|
"\n",
|
|
"1. 点击`File -> Save`或者用`control+s`组合键，确保你最新的的notebook的作业已经保存到谷歌云。\n",
|
|
"2. 执行以下代码确保 `.py` 文件保存回你的谷歌云。"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"import os\n",
|
|
"\n",
|
|
"FOLDER_TO_SAVE = os.path.join('drive/My Drive/', FOLDERNAME)\n",
|
|
"FILES_TO_SAVE = ['daseCV/classifiers/linear_svm.py', 'daseCV/classifiers/linear_classifier.py']\n",
|
|
"\n",
|
|
"for files in FILES_TO_SAVE:\n",
|
|
" with open(os.path.join(FOLDER_TO_SAVE, '/'.join(files.split('/')[1:])), 'w') as f:\n",
|
|
" f.write(''.join(open(files).readlines()))"
|
|
]
|
|
}
|
|
],
|
|
"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": "3.7.0"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 1
|
|
}
|