CS231N assignment1 SVM

以你之姓@ 2022-05-10 07:20 211阅读 0赞

`from cs231n.classifiers.softmax import softmax_loss_naive`  
线性分类器SVM,分成两个部分  
1.a score function that maps the raw data to class scores,也就是所谓的ｆ(w,x)函数  
2.a loss function that quantifies the agreement between the predicted scores and the ground truth labels  
![在这里插入图片描述][70]

##### margin: #####

SVM loss function wants the score of the correct class yi to be larger than the incorrect class scores by at least by Δ (delta). If this is not the case, we will accumulate loss.

##### example #####

![在这里插入图片描述][70 1]

##### 1. loss function #####

cs231n/classifiers/linear\_softmax.py中

#### softmax\_loss\_naive ####

SVM想让正确类别的score比错误类别的score要高出一个固定的margin Δ.  
svm的损失函数计算方法

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

![在这里插入图片描述][70 2]

for i in xrange(num_train):#0-N
        scores = X[i].dot(W) ##1*C  
        correct_class_score = scores[y[i]] 
        for j in xrange(num_classes):# 0-C
          if j == y[i]:
            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

#### softmax\_loss\_vectorized ####

loss

scores = X.dot(W)
      yi_scores = scores[np.arange(scores.shape[0]),y] 
      margins = np.maximum(0, scores - np.matrix(yi_scores).T + 1)
      margins[np.arange(num_train),y] = 0
      loss = np.mean(np.sum(margins, axis=1))
      loss += 0.5 * reg * np.sum(W * W)

\#\#\#\#参考  
[cs231n linear classifier SVM][]  
[https://mlxai.github.io/2017/01/06/vectorized-implementation-of-svm-loss-and-gradient-update.html][https_mlxai.github.io_2017_01_06_vectorized-implementation-of-svm-loss-and-gradient-update.html]

[70]: /images/20220510/732d3621b4234674b9ef65fe938ea686.png
[70 1]: /images/20220510/2a751661e6cc4433a121eba1a3562923.png
[70 2]: /images/20220510/6f7345808f3a47b3af84fe30b7dc9a11.png
[cs231n linear classifier SVM]: https://cs231n.github.io/linear-classify/
[https_mlxai.github.io_2017_01_06_vectorized-implementation-of-svm-loss-and-gradient-update.html]: https://mlxai.github.io/2017/01/06/vectorized-implementation-of-svm-loss-and-gradient-update.html