线性SVM分类器实战

1 概述

基础的理论知识参考线性SVM与Softmax分类器。

代码实现环境：python3

2 数据处理

2.1 加载数据集

将原始数据集放入“data/cifar10/”文件夹下。

### 加载cifar10数据集

import os
import pickle
import random
import numpy as np
import matplotlib.pyplot as plt

def load_CIFAR_batch(filename):
    """
    cifar-10数据集是分batch存储的，这是载入单个batch

    @参数 filename: cifar文件名
    @r返回值: X, Y: cifar batch中的 data 和 labels
    """

    with open(filename,'rb') as f:
        datadict=pickle.load(f,encoding='bytes')

        X=datadict[b'data']
        Y=datadict[b'labels']
        
        X=X.reshape(10000, 3, 32, 32).transpose(0,2,3,1).astype("float")
        Y=np.array(Y)
        
        return X, Y

def load_CIFAR10(ROOT):
    """
    读取载入整个 CIFAR-10 数据集

    @参数 ROOT: 根目录名
    @return: X_train, Y_train: 训练集 data 和 labels
             X_test, Y_test: 测试集 data 和 labels
    """

    xs=[]
    ys=[]

    for b in range(1,6):
        f=os.path.join(ROOT, "data_batch_%d" % (b, ))
        X, Y=load_CIFAR_batch(f)
        xs.append(X)
        ys.append(Y)

    X_train=np.concatenate(xs)
    Y_train=np.concatenate(ys)

    del X, Y

    X_test, Y_test=load_CIFAR_batch(os.path.join(ROOT, "test_batch"))

    return X_train, Y_train, X_test, Y_test

X_train, y_train, X_test, y_test = load_CIFAR10('data/cifar10/') 

print(X_train.shape)
print(y_train.shape)
print(X_test.shape)
print( y_test.shape)

运行结果如下：

(50000, 32, 32, 3)
(50000,)
(10000, 32, 32, 3)
(10000,)

2.2 划分数据集

将加载好的数据集划分为训练集，验证集，以及测试集。

## 划分训练集，验证集，测试集

num_train = 49000
num_val = 1000
num_test = 1000

# Validation set
mask = range(num_train, num_train + num_val)
X_val = X_train[mask]
y_val = y_train[mask]

# Train set
mask = range(num_train)
X_train = X_train[mask]
y_train = y_train[mask]

# Test set
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)

运行结果为：

Train data shape:  (49000, 3072)
Validation data shape:  (1000, 3072)
Test data shape:  (1000, 3072)

2.3 去均值归一化

将划分好的数据集归一化，即：所有划分好的数据集减去均值图像。

# Processing: subtract the mean images
mean_image = np.mean(X_train, axis=0)

X_train -= mean_image
X_val -= mean_image
X_test -= mean_image

# append the bias dimension of ones (i.e. bias trick)
X_train = np.hstack([X_train, np.ones((X_train.shape[0], 1))])#堆叠数组
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))])
print('Train data shape: ', X_train.shape)
print('Validation data shape: ', X_val.shape)
print('Test data shape: ', X_test.shape)

运行结果为：

Train data shape:  (49000, 3073)
Validation data shape:  (1000, 3073)
Test data shape:  (1000, 3073)

3 线性SVM分类器

3.1 定义线性SVM分类器

关键的是线性SVM的梯度推导过程。具体的可以看看这篇文章。

#Define a linear SVM classifier

class LinearSVM(object):
    """ A subclass that uses the Multiclass SVM loss function """
    def __init__(self):
        self.W = None

    def loss_vectorized(self, X, y, reg):
        """
        Structured SVM loss function, naive implementation (with loops).
        Inputs:
        - X: A numpy array of shape (num_train, D) contain the training data
          consisting of num_train samples each of dimension D
        - y: A numpy array of shape (num_train,) contain the training labels,
          where y[i] is the label of X[i]
        - reg: (float) regularization strength
        Outputs:
        - loss: the loss value between predict value and ground truth
        - dW: gradient of W
        """
        
         # Initialize loss and dW
        loss = 0.0
        dW = np.zeros(self.W.shape)
        
        # Compute the loss
        num_train = X.shape[0]
        scores = np.dot(X, self.W)
        correct_score = scores[range(num_train), list(y)].reshape(-1, 1)    
        margin = np.maximum(0, scores - correct_score + 1) # delta = 1
        margin[range(num_train), list(y)] = 0  #分对的损失为0
        loss = np.sum(margin) / num_train + 0.5 * reg * np.sum(self.W * self.W) #reg就是权重lamda
        
        # Compute the dW
        num_classes = self.W.shape[1]
        mask = np.zeros((num_train, num_classes))
        mask[margin > 0] = 1
        mask[range(num_train), list(y)] = 0
        mask[range(num_train), list(y)] = -np.sum(mask, axis=1)
        dW = np.dot(X.T, mask)
        dW = dW / num_train + reg * self.W
        
        return loss, dW
    
    def train(self, X, y, learning_rate = 1e-3, reg = 1e-5, num_iters = 100, 
             batch_size = 200, print_flag = False):
        """
        Train linear SVM classifier using SGD
        Inputs:
        - X: A numpy array of shape (num_train, D) contain the training data
          consisting of num_train samples each of dimension D
        - y: A numpy array of shape (num_train,) contain the training labels,
          where y[i] is the label of X[i], y[i] = c, 0 <= c <= C
        - learning rate: (float) learning rate for optimization
        - reg: (float) regularization strength
        - num_iters: (integer) numbers of steps to take when optimization
        - batch_size: (integer) number of training examples to use at each step
        - print_flag: (boolean) If true, print the progress during optimization
        Outputs:
        - loss_history: A list containing the loss at each training iteration
        """
        
        loss_history = []
        num_train = X.shape[0]
        dim = X.shape[1]
        num_classes = np.max(y) + 1
        
        # Initialize W
        if self.W == None:
            self.W = 0.001 * np.random.randn(dim, num_classes)
        
        # iteration and optimization
        for t in range(num_iters):
            idx_batch = np.random.choice(num_train, batch_size, replace=True)
            X_batch = X[idx_batch]
            y_batch = y[idx_batch]
            loss, dW = self.loss_vectorized(X_batch, y_batch, reg)
            loss_history.append(loss)
            self.W += -learning_rate * dW
            
            if print_flag and t%100 == 0:
                print('iteration %d / %d: loss %f' % (t, num_iters, loss))
        
        return loss_history
    
    def predict(self, X):
        """
        Use the trained weights of linear SVM to predict data labels
        Inputs:
        - X: A numpy array of shape (num_train, D) contain the training data
        Outputs:
        - y_pred: A numpy array, predicted labels for the data in X
        """
        
        y_pred = np.zeros(X.shape[0])
        scores = np.dot(X, self.W)
        y_pred = np.argmax(scores, axis=1)
        
        return y_pred        

3.2 无交叉验证

3.2.1 训练模型

##Stochastic Gradient Descent

svm = LinearSVM()
loss_history = svm.train(X_train, y_train, learning_rate = 1e-7, reg = 2.5e4, num_iters = 2000, 
             batch_size = 200, print_flag = True)

运行结果如下：

iteration 0 / 2000: loss 407.076351
iteration 100 / 2000: loss 241.030820
iteration 200 / 2000: loss 147.135737
iteration 300 / 2000: loss 90.274781
iteration 400 / 2000: loss 56.509895
iteration 500 / 2000: loss 36.654007
iteration 600 / 2000: loss 23.732160
iteration 700 / 2000: loss 16.340341
iteration 800 / 2000: loss 11.538806
iteration 900 / 2000: loss 9.482515
iteration 1000 / 2000: loss 7.414343
iteration 1100 / 2000: loss 6.240377
iteration 1200 / 2000: loss 5.774960
iteration 1300 / 2000: loss 5.569365
iteration 1400 / 2000: loss 5.326023
iteration 1500 / 2000: loss 5.708757
iteration 1600 / 2000: loss 4.731255
iteration 1700 / 2000: loss 5.516500
iteration 1800 / 2000: loss 4.959480
iteration 1900 / 2000: loss 5.447249

3.2.2 预测

# Use svm to predict
# Training set
y_pred = svm.predict(X_train)
num_correct = np.sum(y_pred == y_train)
accuracy = np.mean(y_pred == y_train)
print('Training correct %d/%d: The accuracy is %f' % (num_correct, X_train.shape[0], accuracy))

# Test set
y_pred = svm.predict(X_test)
num_correct = np.sum(y_pred == y_test)
accuracy = np.mean(y_pred == y_test)
print('Test correct %d/%d: The accuracy is %f' % (num_correct, X_test.shape[0], accuracy))

运行结果如下：

Training correct 18799/49000: The accuracy is 0.383653
Test correct 386/1000: The accuracy is 0.386000

3.3 有交叉验证

3.3.1 训练模型

#Cross-validation

learning_rates = [1.4e-7, 1.5e-7, 1.6e-7]
regularization_strengths = [8000.0, 9000.0, 10000.0, 11000.0, 18000.0, 19000.0, 20000.0, 21000.0]

results = {}
best_lr = None
best_reg = None
best_val = -1   # The highest validation accuracy that we have seen so far.
best_svm = None # The LinearSVM object that achieved the highest validation rate.

for lr in learning_rates:
    for reg in regularization_strengths:
        svm = LinearSVM()
        loss_history = svm.train(X_train, y_train, learning_rate = lr, reg = reg, num_iters = 2000)
        y_train_pred = svm.predict(X_train)
        accuracy_train = np.mean(y_train_pred == y_train)
        y_val_pred = svm.predict(X_val)
        accuracy_val = np.mean(y_val_pred == y_val)
        if accuracy_val > best_val:
            best_lr = lr
            best_reg = reg
            best_val = accuracy_val
            best_svm = svm
        results[(lr, reg)] = accuracy_train, accuracy_val
        print('lr: %e reg: %e train accuracy: %f val accuracy: %f' %
              (lr, reg, results[(lr, reg)][0], results[(lr, reg)][1]))
print('Best validation accuracy during cross-validation:
lr = %e, reg = %e, best_val = %f' %
      (best_lr, best_reg, best_val))     

3.3.2 预测

# Use the best svm to test
y_test_pred = best_svm.predict(X_test)
num_correct = np.sum(y_test_pred == y_test)
accuracy = np.mean(y_test_pred == y_test)
print('Test correct %d/%d: The accuracy is %f' % (num_correct, X_test.shape[0], accuracy))

运行结果为：

Test correct 372/1000: The accuracy is 0.372000