线性分类器和神经网络分类器的对比

偏执的太偏执、 2023-07-06 09:58 157阅读 0赞

在这部分对反向传导不是很理解，觉得我以后得 再看其他书籍了，这个视频课真的只适合入门的简单了解

### 1. 训练数据 ###

import numpy as np
    import matplotlib.pyplot as plt
    
    plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
    plt.rcParams['image.interpolation'] = 'nearest'
    plt.rcParams['image.cmap'] = 'gray'
    
    np.random.seed(0)
    N = 100 # number of points per class
    D = 2 # dimensionality
    K = 3 # number of classes
    X = np.zeros((N*K,D))
    y = np.zeros(N*K, dtype='uint8')
    for j in range(K):
      ix = range(N*j,N*(j+1))
      r = np.linspace(0.0,1,N) # radius
      t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta
      X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
      y[ix] = j
    fig = plt.figure()
    plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)
    plt.xlim([-1,1])
    plt.ylim([-1,1])
    plt.show()

运行结果：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70]

### 2.使用线性分类器 ###

#Train a Linear Classifier
    import numpy as np
    import matplotlib.pyplot as plt
    
    
    np.random.seed(0)
    N = 100 # number of points per class
    D = 2 # dimensionality
    K = 3 # number of classes
    X = np.zeros((N*K,D))
    y = np.zeros(N*K, dtype='uint8')
    for j in range(K):
      ix = range(N*j,N*(j+1))
      r = np.linspace(0.0,1,N) # radius
      t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta
      X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
      y[ix] = j
    
    
    W = 0.01 * np.random.randn(D,K)
    b = np.zeros((1,K))
    
    # some hyperparameters
    step_size = 1e-0
    reg = 1e-3 # regularization strength
    
    # gradient descent loop
    num_examples = X.shape[0]
    for i in range(1000):
      #print X.shape
      # evaluate class scores, [N x K]
      scores = np.dot(X, W) + b   #x:300*2 scores:300*3
      #print scores.shape 
      # compute the class probabilities
      exp_scores = np.exp(scores)
      probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K] probs:300*3
      # print(probs.shape)
      # compute the loss: average cross-entropy loss and regularization
      corect_logprobs = -np.log(probs[range(num_examples),y]) #corect_logprobs:300*1
      # print(corect_logprobs.shape)
      data_loss = np.sum(corect_logprobs)/num_examples
      reg_loss = 0.5*reg*np.sum(W*W)
      loss = data_loss + reg_loss
      if i % 100 == 0:
        print("iteration %d: loss %f" % (i, loss))
      
      # compute the gradient on scores
      dscores = probs
      dscores[range(num_examples),y] -= 1
      dscores /= num_examples
      
      # backpropate the gradient to the parameters (W,b)
      dW = np.dot(X.T, dscores)
      db = np.sum(dscores, axis=0, keepdims=True)
      
      dW += reg*W # regularization gradient
      
      # perform a parameter update
      W += -step_size * dW
      b += -step_size * db
      scores = np.dot(X, W) + b
    predicted_class = np.argmax(scores, axis=1)
    print('training accuracy: %.2f' % (np.mean(predicted_class == y)))
    
    h = 0.02
    x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
    y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
                         np.arange(y_min, y_max, h))
    Z = np.dot(np.c_[xx.ravel(), yy.ravel()], W) + b
    Z = np.argmax(Z, axis=1)
    Z = Z.reshape(xx.shape)
    fig = plt.figure()
    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)
    plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)
    plt.xlim(xx.min(), xx.max())
    plt.ylim(yy.min(), yy.max())
    plt.show()

运行结果：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 1]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 2]

### 3.使用神经网络分类器 ###

import numpy as np
    import matplotlib.pyplot as plt
    
    np.random.seed(0)
    N = 100 # number of points per class
    D = 2 # dimensionality
    K = 3 # number of classes
    X = np.zeros((N*K,D))
    y = np.zeros(N*K, dtype='uint8')
    for j in range(K):
      ix = range(N*j,N*(j+1))
      r = np.linspace(0.0,1,N) # radius
      t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta
      X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
      y[ix] = j
      
    h = 100 # size of hidden layer
    W = 0.01 * np.random.randn(D,h)# x:300*2 2*100
    b = np.zeros((1,h))
    W2 = 0.01 * np.random.randn(h,K)
    b2 = np.zeros((1,K))
    
    # some hyperparameters
    step_size = 1e-0
    reg = 1e-3 # regularization strength
    
    # gradient descent loop
    num_examples = X.shape[0]
    for i in range(2000):
      
      # evaluate class scores, [N x K]
      hidden_layer = np.maximum(0, np.dot(X, W) + b) # note, ReLU activation hidden_layer:300*100
      #print hidden_layer.shape
      scores = np.dot(hidden_layer, W2) + b2  #scores:300*3
      #print scores.shape
      # compute the class probabilities
      exp_scores = np.exp(scores)
      probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K]
      #print probs.shape
      
      # compute the loss: average cross-entropy loss and regularization
      corect_logprobs = -np.log(probs[range(num_examples),y])
      data_loss = np.sum(corect_logprobs)/num_examples
      reg_loss = 0.5*reg*np.sum(W*W) + 0.5*reg*np.sum(W2*W2)
      loss = data_loss + reg_loss
      if i % 100 == 0:
        print("iteration %d: loss %f" % (i, loss))
      
      # compute the gradient on scores
      dscores = probs
      dscores[range(num_examples),y] -= 1
      dscores /= num_examples
      
      # backpropate the gradient to the parameters
      # first backprop into parameters W2 and b2
      dW2 = np.dot(hidden_layer.T, dscores)
      db2 = np.sum(dscores, axis=0, keepdims=True)
      # next backprop into hidden layer
      dhidden = np.dot(dscores, W2.T)
      # backprop the ReLU non-linearity
      dhidden[hidden_layer <= 0] = 0
      # finally into W,b
      dW = np.dot(X.T, dhidden)
      db = np.sum(dhidden, axis=0, keepdims=True)
      
      # add regularization gradient contribution
      dW2 += reg * W2
      dW += reg * W
      
      # perform a parameter update
      W += -step_size * dW
      b += -step_size * db
      W2 += -step_size * dW2
      b2 += -step_size * db2
    hidden_layer = np.maximum(0, np.dot(X, W) + b)
    scores = np.dot(hidden_layer, W2) + b2
    predicted_class = np.argmax(scores, axis=1)
    print('training accuracy: %.2f' % (np.mean(predicted_class == y)))
    
    
    h = 0.02
    x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
    y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
                         np.arange(y_min, y_max, h))
    Z = np.dot(np.maximum(0, np.dot(np.c_[xx.ravel(), yy.ravel()], W) + b), W2) + b2
    Z = np.argmax(Z, axis=1)
    Z = Z.reshape(xx.shape)
    fig = plt.figure()
    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)
    plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)
    plt.xlim(xx.min(), xx.max())
    plt.ylim(yy.min(), yy.max())
    plt.show()

运行结果：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 3]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 4]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/2020021721124486.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 1]: https://img-blog.csdnimg.cn/20200217211458508.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 2]: https://img-blog.csdnimg.cn/2020021721152667.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 3]: https://img-blog.csdnimg.cn/20200217213206795.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg_size_16_color_FFFFFF_t_70 4]: https://img-blog.csdnimg.cn/20200217213022449.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjI2MDEwMg==,size_16,color_FFFFFF,t_70