CS231N课程作业Assignment1--SVM
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Assignment1–SVM
作业要求见这里.
主要需要完成 KNN，SVM，Softmax分类器，还有一个两层的神经网络分类器的实现。
数据集CIFAR-10.
SVM原理
SVM(Support Vector Machine，支持向量机)，是一种二类分类模型，其基本模型定义为特征空间上的即那个最大的线性分类器，器学习策略是间隔最大化，最终可转化为一个凸二次规划问题的解决。(线性支持向量机、非线性支持向量机)。
SVM的主要思想是建立一个超平面作为决策曲面，是的正例和反例之间的隔离边缘被最大化。对于二维线性可分情况，令H为把两类训练样本没有错误地分开的分类县，H1、H2分别为过各类中离分类线最近的样本且平行于分类线的直线，它们之间的距离讲座分类间隔。所谓最优分类线就是要求分类线不但能将两类正确分开，而且使分类间隔最大。在高维空间，最优分类线就成为最优分类线。
构建SVM分类器
程序整体框架如下：包括classifiers和datasets文件夹，svm.py、data_utils.py、linear_classifier.py和linear_svm.py
svm.py
from linear_classifier import LinearSVM
import time
import numpy as np #导入numpy的库函数
from datasets.data_utils import load_CIFAR10
import matplotlib.pyplot as plt
from classifiers.linear_svm import *
import math
cifar10_dir = 'E:/cifar-10-batches-py'
X_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)
print('Training data shape: ',X_train.shape)
print('Training labels shape: ',y_train.shape)
print('Test data shape: ',X_test.shape)
print('Test labels shape: ',y_test.shape)
classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']
num_classes = len(classes)
samples_per_class = 7 #每个类别采样个数
for y,cls in enumerate(classes): #(0,plane),y返回元素位置，cls返回元素本身
idxs = np.flatnonzero(y_train==y) #找出标签中y类的位置
idxs = np.random.choice(idxs,samples_per_class,replace=False) #从中随机算出7个样本
for i,idx in enumerate(idxs): #对所选样本的位置和样本所对应的图片在训练集中的位置进行循环
plt_idx = i * num_classes + y + 1 #在子图中所占位置的计算
plt.subplot(samples_per_class,num_classes,plt_idx) #说明要画的子图的编号
plt.imshow(X_train[idx].astype('uint8')) #画图
plt.axis('off')
if i == 0:
plt.title(cls) #写上类别名
plt.show()
num_training = 49000 # 训练集 num_dev会从其中抽取一定数量的图片用于训练，减少训练时间
num_validation = 1000 # 验证集 在不同的学习率和正则参数下使用该验证集获取最高的正确率，最终找到最好的学习率和正则参数
num_test = 1000 # 测试集 在获取到最好的学习率和正则参数之后，测试最终的正确率
num_dev = 500 # 随机训练集 用于实现随机化梯度下降的
mask = range(num_training, num_training + num_validation) # 从训练数据x_train和y_train中获取验证集数据
X_val = X_train[mask]
y_val = y_train[mask]
mask = range(num_training) # 从训练数据x_train和y_train中获取全体训练集数据
X_train = X_train[mask]
y_train = y_train[mask]
mask = np.random.choice(num_training, num_dev, replace=False) # 从num_training中随机选取随机训练集数据
X_dev = X_train[mask]
y_dev = y_train[mask]
mask = range(num_test)
X_test = X_test[mask]
y_test = y_test[mask]
print('Train data shape: ', X_train.shape)
print('Train labels shape: ', y_train.shape)
print('Validation data shape: ', X_val.shape)
print('Validation labels shape: ', y_val.shape)
print('Test data shape: ', X_test.shape)
print('Test labels shape: ', y_test.shape)
# 将x_train，x_val，x_test，x_dev这些n*32*32*3的图片集，转化成n*3072的矩阵；将每张图片拉伸成一维的矩阵，方便后面进行数据处理
X_train = np.reshape(X_train, (X_train.shape[0], -1))
X_val = np.reshape(X_val, (X_val.shape[0], -1))
X_test = np.reshape(X_test, (X_test.shape[0], -1))
X_dev = np.reshape(X_dev, (X_dev.shape[0], -1))
print('Training data shape: ', X_train.shape)
print('Validation data shape: ', X_val.shape)
print('Test data shape: ', X_test.shape)
print('dev data shape: ', X_dev.shape)
mean_image = np.mean(X_train, axis=0)
print(mean_image[:10])
plt.figure(figsize=(4,4))
plt.imshow(mean_image.reshape((32,32,3)).astype('uint8'))
plt.show()
# 将x_train，x_val，x_test，x_dev这些图片集进行去均值处理 ；统一量纲，和归一化操作类似，只是没有再除以方差而已
X_train -= mean_image
X_val -= mean_image
X_test -= mean_image
X_dev -= mean_image
X_train = np.hstack([X_train, np.ones((X_train.shape[0], 1))])
X_val = np.hstack([X_val, np.ones((X_val.shape[0], 1))])
X_test = np.hstack([X_test, np.ones((X_test.shape[0], 1))])
X_dev = np.hstack([X_dev, np.ones((X_dev.shape[0], 1))])
print(X_train.shape, X_val.shape, X_test.shape, X_dev.shape)
W = np.random.randn(3073, 10) * 0.0001
loss, grad = svm_loss_naive(W, X_dev, y_dev, 0.000005)
print('loss: %f' % (loss, ))
tic = time.time()
loss_naive, grad_naive = svm_loss_naive(W, X_dev, y_dev, 0.000005)
toc = time.time()
print('Naive loss: %e computed in %fs' % (loss_naive, toc - tic))
tic = time.time()
loss_vectorized, _ = svm_loss_vectorized(W, X_dev, y_dev, 0.000005)
toc = time.time()
print('Vectorized loss: %e computed in %fs' % (loss_vectorized, toc - tic))
print('difference: %f' % (loss_naive - loss_vectorized))
tic = time.time()
_, grad_naive = svm_loss_naive(W, X_dev, y_dev, 0.000005)
toc = time.time()
print('Naive loss and gradient: computed in %fs' % (toc - tic))
tic = time.time()
_, grad_vectorized = svm_loss_vectorized(W, X_dev, y_dev, 0.000005)
toc = time.time()
print('Vectorized loss and gradient: computed in %fs' % (toc - tic))
difference = np.linalg.norm(grad_naive - grad_vectorized, ord='fro')
print('difference: %f' % difference)
svm = LinearSVM()
tic = time.time()
loss_hist = svm.train(X_train, y_train, learning_rate=1e-7, reg=2.5e4,num_iters=1500, verbose=True)
toc = time.time()
print('That took %fs' % (toc - tic))
plt.plot(loss_hist)
plt.xlabel('Iteration number')
plt.ylabel('Loss value')
plt.show()
y_train_pred = svm.predict(X_train)
print('training accuracy: %f' % (np.mean(y_train == y_train_pred), ))
y_val_pred = svm.predict(X_val)
print('validation accuracy: %f' % (np.mean(y_val == y_val_pred), ))
#调参
#两个参数，学习率；正则化强度
learning_rates = [1e-7, 3e-7,5e-7,9e-7]
regularization_strengths = [2.5e4, 1e4,3e4,2e4]
results =
best_val = -1
best_svm = None
for learning_rate in learning_rates: # 循环执行代码；对不同的学习率以及正则化强度进行测试
for regularization_strength in regularization_strengths:
svm = LinearSVM() # learning_rate学习率；reg正则化强度；num_iters步长值；batch_size每一步使用的样本数量；verbose若为真则打印过程
loss_hist = svm.train(X_train, y_train, learning_rate=learning_rate, reg=regularization_strength,num_iters=1500, verbose=True)
y_train_pred = svm.predict(X_train)
y_val_pred = svm.predict(X_val)
y_train_acc = np.mean(y_train_pred==y_train)
y_val_acc = np.mean(y_val_pred==y_val)
results[(learning_rate,regularization_strength)] = [y_train_acc, y_val_acc]
if y_val_acc > best_val: # 判断优略
best_val = y_val_acc
best_svm = svm # 保存当前模型
for lr, reg in sorted(results):
train_accuracy, val_accuracy = results[(lr, reg)] # 存储数据
print('lr %e reg %e train accuracy: %f val accuracy: %f' % (lr, reg, train_accuracy, val_accuracy))
print('best validation accuracy achieved during cross-validation: %f' % best_val)
x_scatter = [math.log10(x[0]) for x in results]
y_scatter = [math.log10(x[1]) for x in results]
marker_size = 100
colors = [results[x][0] for x in results]
plt.subplot(1, 2, 1)
plt.scatter(x_scatter, y_scatter, marker_size, c=colors)
plt.colorbar()
plt.xlabel('log learning rate')
plt.ylabel('log regularization strength')
plt.title('CIFAR-10 training accuracy')
colors = [results[x][1] for x in results] # default size of markers is 20
plt.subplot(1, 2, 2)
plt.scatter(x_scatter, y_scatter, marker_size, c=colors)
plt.colorbar()
plt.xlabel('log learning rate')
plt.ylabel('log regularization strength')
plt.title('CIFAR-10 validation accuracy')
plt.show()
y_test_pred = best_svm.predict(X_test)
test_accuracy = np.mean(y_test == y_test_pred)
print('linear SVM on raw pixels final test set accuracy: %f' % test_accuracy)
#得到最优W时，W的可视化结果数据 W的图像可以看出权重的高低
w = best_svm.W[:-1,:]
w = w.reshape(32, 32, 3, 10)
w_min, w_max = np.min(w), np.max(w)
classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck'] # 类别划分 列表
for i in range(10):
plt.subplot(2, 5, i + 1)
wimg = 255.0 * (w[:, :, :, i].squeeze() - w_min) / (w_max - w_min)
plt.imshow(wimg.astype('uint8'))
plt.axis('off')
plt.title(classes[i])
plt.show() # W最终学习成的图片
linear_svm.py
from builtins import range
import numpy as np
from random import shuffle
def svm_loss_naive(W, X, y, reg): # 使用循环实现的SVM loss函数；W ：一个numpy 数组，维数为(D,C),存储权重;D为特征向量的维度，C为分类类别的数量
dW = np.zeros(W.shape) # 创建一个梯度 # X ：一个numpy数组，维数为（N,D），存储一小批数据
num_classes = W.shape[1] # 划分的种类 # y : 一个numpy数组，维数为(N,),存储训练标签
num_train = X.shape[0] # 训练样本的数量 # reg ：float，正则化强度
loss = 0.0 # 初始化损失
for i in range(num_train): #分别求每个训练样本的损失
scores = X[i].dot(W) # 计算每个样本的分数；计算当前W和当前训练图片X[i]在各个图片种类下的分数scores
correct_class_score = scores[y[i]] # 获得当前训练图片X[i]真实图片种类的分数correct_class_score
for j in range(num_classes): # 计算损失
if j == y[i]: # 如果当前的图片种类j，就是当前训练图片X[i]真实的图片种类y[i]，那么由前面损失函数的定义可知，我们不需要继续执行
continue # 如果1不成立，我们就能计算出对于当前训练图片X[i]，在图片种类j下的损失分量margin
margin = scores[j] - correct_class_score + 1 # hinge loss(max margin)
if margin > 0: # 由前面损失函数的定义可知loss只需要大于0的margin，所以如果margin小于0，那么就当0处理，接下来就没必要继续了
loss += margin
dW[:,j] += X[i]
dW[:, y[i]] += (-X[i])
loss /= num_train
dW /= reg * W # 加入正则化
return loss, dW # loss : 损失函数的值 ； dW : 权重W的梯度，和W大小相同的array
def svm_loss_vectorized(W, X, y, reg): # 结构化的SVM损失函数，使用向量来实现
dW = np.zeros(W.shape) # 初始化梯度为0
num_classes = W.shape[1]
num_train = X.shape[0]
loss = 0.0
scores = X.dot(W)
correct_class_scores = scores[range(num_train), list(y)].reshape(-1,1) #(N, 1)
margins = np.maximum(0, scores - correct_class_scores +1)
margins[range(num_train), list(y)] = 0
loss = np.sum(margins) / num_train + 0.5 * reg * np.sum(W * W)
coeff_mat = np.zeros((num_train, num_classes))
coeff_mat[margins > 0] = 1
coeff_mat[range(num_train), list(y)] = 0
coeff_mat[range(num_train), list(y)] = -np.sum(coeff_mat, axis=1)
dW = (X.T).dot(coeff_mat)
dW = dW/num_train + reg*W
return loss, dW
data_utils.py
from __future__ import print_function
from builtins import range
from six.moves import cPickle as pickle
import numpy as np
import os
from imageio import imread
import platform
def load_pickle(f):
version = platform.python_version_tuple()
if version[0] == '2':
return pickle.load(f)
elif version[0] == '3':
return pickle.load(f, encoding='latin1')
raise ValueError("invalid python version: ".format(version))
def load_CIFAR_batch(filename<以上是关于CS231N课程作业Assignment1--SVM的主要内容，如果未能解决你的问题，请参考以下文章
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