cs231n svm代码解析
from cs231n.classifiers.linear_svm import svm_loss_naive
import time
# generate a random SVM weight matrix of small numbers
W = np.random.randn(3073, 10) * 0.0001
#W生成了一个随机的W权重矩阵是 3073 X 10的矩阵
#X_dev是一个500 X 3073的输入向量
#y_dev是500X1的答案
loss, grad = svm_loss_naive(W, X_dev, y_dev, 0.000005)
print('loss: %f' % (loss, ))
def svm_loss_naive(W, X, y, reg):
"""
Structured SVM loss function, naive implementation (with loops).
Inputs have dimension D, there are C classes, and we operate on minibatches
of N examples.
Inputs:
- W: A numpy array of shape (D, C) containing weights.
- X: A numpy array of shape (N, D) containing a minibatch of data.
- y: A numpy array of shape (N,) containing training labels; y[i] = c means
that X[i] has label c, where 0 <= c < C.
- reg: (float) regularization strength
Returns a tuple of:
- loss as single float
- gradient with respect to weights W; an array of same shape as W
"""
#dW是3073X10的0矩阵
dW = np.zeros(W.shape) # initialize the gradient as zero
# compute the loss and the gradient
num_classes = W.shape[1] #10
num_train = X.shape[0] #500
loss = 0.0
for i in range(num_train):
scores = X[i].dot(W)
#用第i张图片的向量点乘矩阵W得到权重就是分数，y=xw，这个y是预测的分数向量，不用b了，开始通过换元转换为y=xw了
correct_class_score = scores[y[i]]
#y是标签，可以得到正确得分的标签
for j in range(num_classes):
if j == y[i]:
continue
margin = scores[j] - correct_class_score + 1 # note delta = 1
#Li=max(0,w0*wi-w1*xi+1)+max(0,w2*xi-w1*xi+1)
#S0-S1 S2-S1
#对于正确的标签类求导 dLi/dwi = -(xi+xi+...+xi)所以对应 dW[:, y[i]] += -X[i]
#对于不是正确的标签类求导 dLi/dwj(j!=i) = xi 对应 dW[:, j] += X[i]
if margin > 0: #margin是指示函数成立的时候求导不是等于0
dW[:, y[i]] += -X[i]
dW[:, j] += X[i]
loss += margin
#上述一系列操作实际就是用的svm损失函数公式
#Li = 求和（max(0,预测的-正确的+1））
# Right now the loss is a sum over all training examples, but we want it
# to be an average instead so we divide by num_train.
loss /= num_train
dW /= num_train
# Add regularization to the loss.
loss += reg * np.sum(W * W)
#正则化
#############################################################################
# TODO: #
# Compute the gradient of the loss function and store it dW. #
# Rather than first computing the loss and then computing the derivative, #
# it may be simpler to compute the derivative at the same time that the #
# loss is being computed. As a result you may need to modify some of the #
# code above to compute the gradient. #
#############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
# 正则化项 aW^2 求导2aW
dW += 2*reg*W
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
return loss, dW
下面是向量形式
def svm_loss_vectorized(W, X, y, reg):
"""
Structured SVM loss function, vectorized implementation.
Inputs and outputs are the same as svm_loss_naive.
"""
#W生成了一个随机的W权重矩阵是 3073 X 10的矩阵
#X_dev是一个500 X 3073的输入向量
#y_dev是500X1的答案
loss = 0.0
dW = np.zeros(W.shape) # initialize the gradient as zero
#dW 是 3073 X 10
#############################################################################
# TODO: #
# Implement a vectorized version of the structured SVM loss, storing the #
# result in loss. #
#############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
num_train = X.shape[0] #500
scores = X.dot(W)#500 X 10
# scores[range(num_train), [y]]
# 这个是取前num_train行 y是一个ndarry的向量 得到的是500 X 1 的矩阵
# 这句代码的意思是，前num_train的每一行，第一行获取y的第一个位置的列
#第二行的y的第二个位置的列，
#可以推测出位500个测试集正确的得分 .T转置
#scores - scores[range(num_train), [y]].T + 1
#通过广播可以出来结果，如果相减后 结果小于0，就置为0 这个就是svm损失函数的计算
loss_tmp = np.maximum(0, scores - scores[range(num_train), [y]].T + 1)
loss_tmp[range(scores.shape[0]), y] = 0
# loss_tmp[range(scores.shape[0]), y] = 0
# 把每个测试集合 正确得分的位置 都变为0 这一点是对的，因为在计算svm损失函数
# 把正确的类别 不参与计算，排除在外的，所以设置为0 这个是正确的。
loss = np.sum(loss_tmp) / num_train + reg*np.sum(W**2)
#上面加上了正则化 没什么好说的
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
#############################################################################
# TODO: #
# Implement a vectorized version of the gradient for the structured SVM #
# loss, storing the result in dW. #
# #
# Hint: Instead of computing the gradient from scratch, it may be easier #
# to reuse some of the intermediate values that you used to compute the #
# loss. #
#############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
#返回一个用1填充的跟输入 形状和类型 一致的数组。 loss_tmp
#dloss_tmp 是500X10的矩阵 里面每个数据都除以numtrain500之后 都变成0.02填充
dloss_tmp = np.ones_like(loss_tmp) / num_train
dscores = np.zeros_like(scores)
dscores[loss_tmp>0] = 1 #对于一般的 变为1
dscores[range(num_train), y] = -np.sum(dscores, axis=1)#对于特殊的，先将每一列加起来 然后减去
dW = X.T.dot(dscores)
dW += 2*reg*W
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
return loss, dW
```