SVM的代码实现-python

Posted 2021-01-27 深度预习

隔了好久木有更新了，因为发现自己numpy的很多操作都忘记了，加上最近有点忙.。。

接着上次

我们得到的迭代函数为

 

首先j != yi

 

j = yi

import numpy as np
def svm_loss_naive(W, X, y, reg):
    """
    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]:    #根据公式，正确的那个不用算
                continue
            # 叠加margin
            margin = scores[j] - correct_class_score + 1   # note delta = 1
            if margin > 0:
                loss += margin
                dW[:, y[i]] += -X[i, :]     #  根据公式：∇Wyi Li = - xiT(∑j≠yi1(xiWj - xiWyi +1>0)) + 2λWyi 
                dW[:, j] += X[i, :]         #  根据公式： ∇Wj Li = xiT 1(xiWj - xiWyi +1>0) + 2λWj , (j≠yi)
    # 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
    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
    scores = X.dot(W)        # N by C
    num_train = X.shape[0]
    num_classes = W.shape[1]
    scores_correct = scores[np.arange(num_train), y]   # 1 by N
    scores_correct = np.reshape(scores_correct, (num_train, 1))  # N by 1
    margins = scores - scores_correct + 1.0     # N by C
    margins[np.arange(num_train), y] = 0.0
    margins[margins <= 0] = 0.0
    loss += np.sum(margins) / num_train
    loss += 0.5 * reg * np.sum(W * W)
    # compute the gradient
    margins[margins > 0] = 1.0
    row_sum = np.sum(margins, axis=1)                  # 1 by N
    margins[np.arange(num_train), y] = -row_sum        
    dW += np.dot(X.T, margins)/num_train + reg * W     # D by C

    return loss, dW    

　　

还没试一下，近期试一下这个的结果