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linear_svm.py
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linear_svm.py
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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 range(num_train):
scores = X[i].dot(W)
correct_class_score = scores[y[i]]
count_above_margin = 0
for j in range(num_classes):
if j == y[i]:
continue
margin = scores[j] - correct_class_score + 1 # note delta = 1
if margin > 0:
count_above_margin += 1
loss += margin
dW[:, j] = dW[:, j] + X[i, :]
dW[:, y[i]]= dW[:, y[i]] - X[i, :] * count_above_margin
# 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
# Add regularization to the loss.
loss += reg * np.sum(W * 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. #
#############################################################################
dW = dW / num_train + 2 * reg * W
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 = np.dot(X, W)
correct_class_scores = np.choose(y, scores.T)
scores_fil = scores.copy()
scores_fil[range(scores.shape[0]), y] -= 1
scores_margin = scores_fil - correct_class_scores[..., np.newaxis] + 1
scores_margin[scores_margin < 0] = 0
num_train = X.shape[0]
loss = np.sum(scores_margin) / num_train
loss += reg * np.sum(W * W)
#############################################################################
# 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. #
#############################################################################
epsilon = np.finfo(np.float).eps
gra_indicator = (scores_margin > epsilon).astype(float)
sum_ind = gra_indicator.sum(1)
gra_indicator[range(gra_indicator.shape[0]), y] = -sum_ind
dW = np.dot(X.T, gra_indicator)
dW = dW / num_train + 2 * reg * W
return loss, dW