线性Softmax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 数据预处理

2.1 加载数据

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，测试集。

# 划分训练集，验证集，测试集
num_train = 49000
num_val = 1000
num_test = 1000
num_dev = 500#也是验证集，调节超参数使用

# 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]

# Development set
mask = np.random.choice(num_train, num_dev, replace=False)
X_dev = X_train[mask]
y_dev = y_train[mask]

#Reshape the images data into rows

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('Train data shape: ', X_train.shape)
print('Validation data shape: ', X_val.shape)
print('Test data shape: ', X_test.shape)
print('Development data shape: ', X_dev.shape)

运行结果如下：

Train data shape:  (49000, 3072)
Validation data shape:  (1000, 3072)
Test data shape:  (1000, 3072)
Development data shape:  (500, 3072)

2.3 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
X_dev -= mean_image

3 线性Softmax分类器

3.1 定义线性Softmax分类器

#Define a linear Softmax classifier

class Softmax(object):
    def __init__(self):
        self.W = None
    
    def loss_vectorized(self, X, y, reg):
        """
        Structured Softmax loss function, vectorized implementation (without 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
        Return:
        - 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 and dW
        num_train = X.shape[0]
        num_classes = self.W.shape[1]
        
        # loss
        scores = np.dot(X, self.W)
        scores -= np.max(scores, axis=1).reshape(-1, 1)
        softmax_output = np.exp(scores) / np.sum(np.exp(scores), axis=1).reshape(-1, 1)
        loss = np.sum(-np.log(softmax_output[range(softmax_output.shape[0]), list(y)]))
        loss /= num_train
        loss += 0.5 * reg * np.sum(self.W * self.W)
        
        # dW
        dS = softmax_output
        dS[range(dS.shape[0]), list(y)] += -1
        dW = np.dot(X.T, dS)
        dW /= num_train
        dW += 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 Softmax 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 Softmax 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

# 训练
softmax = Softmax()
loss_history = softmax.train(X_train, y_train, learning_rate = 1e-7, reg = 2.5e4, num_iters = 1500, 
             batch_size = 200, print_flag = True)

运行结果如下：

iteration 0 / 1500: loss 386.819945
iteration 100 / 1500: loss 233.345487
iteration 200 / 1500: loss 141.912560
iteration 300 / 1500: loss 86.616391
iteration 400 / 1500: loss 53.114667
iteration 500 / 1500: loss 32.912990
iteration 600 / 1500: loss 20.637937
iteration 700 / 1500: loss 13.341617
iteration 800 / 1500: loss 8.934886
iteration 900 / 1500: loss 6.200619
iteration 1000 / 1500: loss 4.516009
iteration 1100 / 1500: loss 3.514955
iteration 1200 / 1500: loss 2.883086
iteration 1300 / 1500: loss 2.538239
iteration 1400 / 1500: loss 2.365773

3.2.2 预测模型

# Training set
y_pred = softmax.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 = softmax.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 17246/49000: The accuracy is 0.351959
Test correct 358/1000: The accuracy is 0.358000

3.3 有交叉验证

3.3.1 训练模型

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_softmax = None # The LinearSVM object that achieved the highest validation rate.

for lr in learning_rates:
    for reg in regularization_strengths:
        softmax = Softmax()
        loss_history = softmax.train(X_train, y_train, learning_rate = lr, reg = reg, num_iters = 3000)
        y_train_pred = softmax.predict(X_train)
        accuracy_train = np.mean(y_train_pred == y_train)
        y_val_pred = softmax.predict(X_val)
        accuracy_val = np.mean(y_val_pred == y_val)
        results[(lr, reg)] = accuracy_train, accuracy_val
        if accuracy_val > best_val:
            best_lr = lr
            best_reg = reg
            best_val = accuracy_val
            best_softmax = softmax
        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)) 

运行结果为：

lr: 1.400000e-07 reg: 8.000000e+03 train accuracy: 0.378184 val accuracy: 0.391000
lr: 1.400000e-07 reg: 9.000000e+03 train accuracy: 0.374714 val accuracy: 0.387000
lr: 1.400000e-07 reg: 1.000000e+04 train accuracy: 0.376000 val accuracy: 0.391000
lr: 1.400000e-07 reg: 1.100000e+04 train accuracy: 0.373898 val accuracy: 0.387000
lr: 1.400000e-07 reg: 1.800000e+04 train accuracy: 0.360347 val accuracy: 0.373000
lr: 1.400000e-07 reg: 1.900000e+04 train accuracy: 0.354612 val accuracy: 0.379000
lr: 1.400000e-07 reg: 2.000000e+04 train accuracy: 0.357184 val accuracy: 0.379000
lr: 1.400000e-07 reg: 2.100000e+04 train accuracy: 0.357061 val accuracy: 0.380000
lr: 1.500000e-07 reg: 8.000000e+03 train accuracy: 0.378633 val accuracy: 0.397000
lr: 1.500000e-07 reg: 9.000000e+03 train accuracy: 0.377918 val accuracy: 0.399000
lr: 1.500000e-07 reg: 1.000000e+04 train accuracy: 0.376347 val accuracy: 0.383000
lr: 1.500000e-07 reg: 1.100000e+04 train accuracy: 0.374469 val accuracy: 0.391000
lr: 1.500000e-07 reg: 1.800000e+04 train accuracy: 0.362714 val accuracy: 0.373000
lr: 1.500000e-07 reg: 1.900000e+04 train accuracy: 0.358633 val accuracy: 0.370000
lr: 1.500000e-07 reg: 2.000000e+04 train accuracy: 0.358939 val accuracy: 0.373000
lr: 1.500000e-07 reg: 2.100000e+04 train accuracy: 0.360367 val accuracy: 0.379000
lr: 1.600000e-07 reg: 8.000000e+03 train accuracy: 0.378143 val accuracy: 0.397000
lr: 1.600000e-07 reg: 9.000000e+03 train accuracy: 0.372449 val accuracy: 0.386000
lr: 1.600000e-07 reg: 1.000000e+04 train accuracy: 0.376184 val accuracy: 0.379000
lr: 1.600000e-07 reg: 1.100000e+04 train accuracy: 0.369776 val accuracy: 0.377000
lr: 1.600000e-07 reg: 1.800000e+04 train accuracy: 0.359735 val accuracy: 0.378000
lr: 1.600000e-07 reg: 1.900000e+04 train accuracy: 0.359653 val accuracy: 0.374000
lr: 1.600000e-07 reg: 2.000000e+04 train accuracy: 0.356041 val accuracy: 0.370000
lr: 1.600000e-07 reg: 2.100000e+04 train accuracy: 0.353694 val accuracy: 0.370000
Best validation accuracy during cross-validation:
lr = 1.500000e-07, reg = 9.000000e+03, best_val = 0.399000

3.3.2 预测模型

#Use the best softmax to test

y_pred = best_softmax.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, num_test, accuracy))

运行结果如下：

Test correct 375/1000: The accuracy is 0.375000

补充：线性SVM分类器与线性Softmax分类器只是损失函数不一样！！！