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 pltdef 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, Ydef 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_testX_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 classifierclass 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 Descentsvm = 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-validationlearning_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:\nlr = %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
