人工智能实战_第四次作业_王涛

一丶作业要求

标题	内容
这个作业属于哪个课程	班级博客的链接
这个作业的要求在哪里	作业要求的链接
我在这个课程的目标是	完成一个完整的项目，学以致用
这个作业在哪个具体方面帮助我实现目标	帮助我了解反向传播

二、解决方法

1) 训练一个逻辑与门和逻辑或门

有时候不想写太多函数，几行就够了。
以下为Sigmoid + learning_rate = 1.

import numpy as np

np.random.seed(42)
X_and = np.array([[0, 0],[0, 1],[1, 0],[1, 1]])
y_and = np.array([0, 0, 0, 1])
y_and_one_hot = np.zeros((4, 2))
y_and_one_hot[np.arange(4),y_and]=1

weights = np.sqrt(2/3)*np.random.randn(2, 2)
bias = np.ones((1, 2))
loss = np.infty
while loss > 1e-2:
    output = 1/(1 + np.exp(-np.dot(X_and, weights)-bias))
    weights -= np.dot(X_and.T ,(output - y_and_one_hot))
    bias -= np.mean(output-y_and_one_hot, axis=0, keepdims=True)
    loss = -np.mean(np.log(output)*y_and_one_hot)
#output:
#array([[9.99980695e-01, 1.99816334e-05],
#       [9.75014897e-01, 2.52661750e-02],
#       [9.75014897e-01, 2.52661750e-02],
#       [2.85591765e-02, 9.71119454e-01]])
#loss:0.009991269981324791

X_or = np.array([[0, 0],[0, 1],[1, 0],[1, 1]])
y_or = np.array([0, 1, 1, 1])
y_or_one_hot = np.zeros((4, 2))
y_or_one_hot[np.arange(4),y_or]=1
weights = np.sqrt(2/3)*np.random.randn(2, 2)
bias = np.ones((1, 2))
loss = np.infty
while loss > 1e-2:
    output = 1/(1 + np.exp(-np.dot(X_or, weights)-bias))
    weights -= np.dot(X_or.T ,(output - y_or_one_hot))
    bias -= np.mean(output-y_or_one_hot, axis=0, keepdims=True)
    loss = -np.mean(np.log(output[np.arange(4), y_or]))
#output
#array([[9.73856986e-01, 2.69389503e-02],
#       [6.49497719e-03, 9.93314951e-01],
#       [6.48613192e-03, 9.93311743e-01],
#       [1.14572236e-06, 9.99998745e-01]])
#loss:0.009977572598324626

2)二分类可视化

core code

def ShowData(X,Y, W, B):
    for i in range(X.shape[0]):
        if Y[i,0] == 0:
            plt.plot(X[i,0], X[i,1], '.', c='r')
        elif Y[i,0] == 1:
            plt.plot(X[i,0], X[i,1], '^', c='g')
        # end if
    # end for
    plt.axis([-0.1, 1.1, -0.1, 1.1])
    w12 = -W[0,0]/W[1,0]
    b12 = -B[0,0]/W[1,0]

    x = np.linspace(0,1,10)
    y = x*w12 + b12
    plt.plot(x,y)
    plt.show()

引自：Microsoft-ai-edu

与门：

或门：

3)经典多分类svm

def svm_loss(x, y):
    """
    Computes the loss and gradient using for multiclass SVM classification.

    Inputs:
    - x: Input data, of shape (N, C) where x[i, j] is the score for the jth
      class for the ith input.
    - y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
      0 <= y[i] < C

    Returns a tuple of:
    - loss: Scalar giving the loss
    - dx: Gradient of the loss with respect to x
    """
    N = x.shape[0]
    correct_class_scores = x[np.arange(N), y]
    margins = np.maximum(0, x - correct_class_scores[:, np.newaxis] + 1.0)
    margins[np.arange(N), y] = 0
    loss = np.sum(margins) / N
    num_pos = np.sum(margins > 0, axis=1)
    dx = np.zeros_like(x)
    dx[margins > 0] = 1
    dx[np.arange(N), y] -= num_pos
    dx /= N
    return loss, dx