# 机器学习基础干货——线性分类（中）

## Multiclass Support Vector Machine Loss

def L_i(x, y, W):   """  unvectorized version. Compute the multiclass svm loss for a single example (x,y)  - x is a column vector representing an image (e.g. 3073 x 1 in CIFAR-10)    with an appended bias dimension in the 3073-rd position (i.e. bias trick)  - y is an integer giving index of correct class (e.g. between 0 and 9 in CIFAR-10)  - W is the weight matrix (e.g. 10 x 3073 in CIFAR-10)  """   delta = 1.0 # see notes about delta later in this section   scores = W.dot(x) # scores becomes of size 10 x 1, the scores for each class   correct_class_score = scores[y]   D = W.shape[0] # number of classes, e.g. 10   loss_i = 0.0   for j in xrange(D): # iterate over all wrong classes     if j == y:       # skip for the true class to only loop over incorrect classes       continue     # accumulate loss for the i-th example     loss_i += max(0, scores[j] - correct_class_score + delta)   return loss_idef L_i_vectorized(x, y, W):   """  A faster half-vectorized implementation. half-vectorized  refers to the fact that for a single example the implementation contains  no for loops, but there is still one loop over the examples (outside this function)  """   delta = 1.0   scores = W.dot(x)   # compute the margins for all classes in one vector operation   margins = np.maximum(0, scores - scores[y] + delta)   # on y-th position scores[y] - scores[y] canceled and gave delta. We want   # to ignore the y-th position and only consider margin on max wrong class   margins[y] = 0   loss_i = np.sum(margins)   return loss_idef L(X, y, W):   """  fully-vectorized implementation :  - X holds all the training examples as columns (e.g. 3073 x 50,000 in CIFAR-10)  - y is array of integers specifying correct class (e.g. 50,000-D array)  - W are weights (e.g. 10 x 3073)  """   # evaluate loss over all examples in X without using any for loops   # left as exercise to reader in the assignment