cs231n_Linear_svm
Linear_svm原理
SVM损失：计算了所有不正确的例子，将所有不正确类别的评分与正确类别评分之差再加1，将得到的数值与0比较，取二者最大，然后将所有数值进行求和。
计算分数：
s
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W
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s=f(x,W)=Wx
s=f(x,W)=Wx
计算完全损失（有正则项）：
代码
主要是矩阵实现程序
import numpy as np
from random import shuffle
from past.builtins import xrange
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 = np.zeros(W.shape) # initialize the gradient as zero
# compute the loss and the gradient
num_classes = W.shape[1]
num_train = X.shape[0]
loss = 0.0
for i in xrange(num_train):
scores = X[i].dot(W)
correct_class_score = scores[y[i]]
for j in xrange(num_classes):
if j == y[i]:
continue
margin = scores[j] - correct_class_score + 1 # note delta = 1
if margin > 0:
loss += margin
dW[:,y[i]]+=-X[i].T
dW[:,j] +=X[i].T
# 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)
dW += 2*reg*W
#############################################################################
# TODO: #
# Compute the gradient of the loss function and store it dW. #
# Rather that 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. #
#############################################################################
return loss, dW
def svm_loss_vectorized(W, X, y, reg):
"""
Structured SVM loss function, vectorized implementation.
Inputs and outputs are the same as svm_loss_naive.
"""
loss = 0.0
dW = np.zeros(W.shape) # initialize the gradient as zero
#############################################################################
# TODO: #
# Implement a vectorized version of the structured SVM loss, storing the #
# result in loss. #
#############################################################################
# scores = X.dot(W)
# num_train = X.shape[0]
# correct_class_score = scores[np.arange(num_train),y]
# correct_class_score = np.reshape(correct_class_score,(num_train,-1))
# margin = scores - correct_class_score + 1
# np.maximum(margin,0) # 判断是否大于0
# margin[np.arange(num_train),y]=0
# loss += np.sum(margin)/num_train
# loss += reg * np.sum(W*W)
scores = X.dot(W)
# num_classes = W.shape[1]
num_train = X.shape[0]
correct_class_score = scores[np.arange(num_train),y]
correct_class_score = np.reshape(correct_class_score,(num_train,-1))
margins = scores - correct_class_score + 1
margins = np.maximum(margins,0)
#然后这里计算了j=y[i]的情形，所以把他们置为0
margins[np.arange(num_train),y] = 0
loss += np.sum(margins) / num_train
loss += reg * np.sum(W*W)
#############################################################################
# END OF YOUR CODE #
#############################################################################
#############################################################################
# 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. #
#############################################################################
# num_classes = W.shape[1]
# mask_margin = np.zeros((num_train, num_classes)) # where margin[i,j]>0=1
# mask_margin[margin>0] = 1
# mask_XW = np.ones((num_train, num_classes))
# mask_XW = mask_XW * mask_margin
# y_sum = np.sum(mask_margin, axis=1)
# print(y_sum.shape)
# mask_XW[np.arange(num_train), y] -= y_sum
# dW = np.dot(X.T, mask_XW)/num_train
# dW += 2 * reg * W
margins[margins > 0] = 1
margins[margins <=0] = 0
row_sum = np.sum(margins, axis=1)
margins[np.arange(num_train),y] -= row_sum
dW = np.dot(X.T, margins)
dW /= num_train
dW += 2*reg*W
#############################################################################
# END OF YOUR CODE #
#############################################################################
return loss, dW
小tips
- numpy可以直接两重索引替换值
arr[arr1,arr2] = 0，即使得arr[arr1[0]][arr2[0]]=0, arr[arr1[1]][arr2[1]]=0…