import numpy as np
from random import shuffle
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)#X[i]=[2,5,4,8,9,9,4,5,5], W=D*C, Scores=[c1 c2 c3 c4 c5 c6 ...cc]
correct_class_score = scores[y[i]]#correct_class_score= > scores[y[i]]=>scores[y[1]]=scores[6]=c6
for j in xrange(num_classes):#num_classes=C j=1,2,3,4,5,6,...,c
if j == y[i]:#if 1 == y[1]=6, go------
continue
margin = scores[j] - correct_class_score + 1 # note delta = 1
if margin > 0:
loss += margin
dW[:,j] += X[i].T
dW[:,y[i]] += -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 += 0.5 * reg * np.sum(W * W)
dW += 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. #
#############################################################################
num_train = X.shape[0]
num_classes = W.shape[1]
scores = X.dot(W)
correct_class_scores = scores[range(num_train), list(y)].reshape(-1,1) #(N, 1)
margins = np.maximum(0, scores - correct_class_scores +1)
margins[range(num_train), list(y)] = 0
loss = np.sum(margins) / num_train + 0.5 * reg * np.sum(W * W)
#pass
#############################################################################
# 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. #
#############################################################################
coeff_mat = np.zeros((num_train, num_classes))
coeff_mat[margins > 0] = 1
coeff_mat[range(num_train), list(y)] = 0
coeff_mat[range(num_train), list(y)] = -np.sum(coeff_mat, axis=1)
dW = (X.T).dot(coeff_mat)
dW = dW/num_train + reg*W
#pass
#############################################################################
# END OF YOUR CODE #
#############################################################################
return loss, dW
