Coursera吴恩达机器学习ML-week4-ex3多分类及神经网络-python实现

很多函数或者内部的一些计算其实没用，但是因为是对应matlab上的作业，所以有的部分会显得多余
不过对于图像的呈现就略过了，个人认为还是先熟悉算法为主，这样进度也快点

task1多分类

import numpy as np
import pandas as pd
#import matplotlib.pyplot as plt 不画图也就用不到了
#import matplotlib
from scipy.io import loadmat
from sklearn.metrics import classification_report
data = loadmat('ex3data1.mat')
#data['X'].shape=(5000, 400), data['y'].shape=(5000, 1)
#共5000张20*20的数字图片，y是对应的tag

def sigmoid(z):
    return 1 / (1 + np.exp(-z))
def cost(theta, X, y, lr):
    theta = np.matrix(theta)
    X = np.matrix(X)
    y = np.matrix(y)
    first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
    second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
    return np.sum(first - second) / len(X)

def gradient(theta, X, y, lr):
    theta = np.matrix(theta)
    X = np.matrix(X)
    y = np.matrix(y)
    
    parameters = int(theta.ravel().shape[1])#theta总个数  
    error = sigmoid(X * theta.T) - y  
   
    grad = theta-((X.T * error) / len(X)).T + ((lr / len(X)) * theta)
    grad[0,0] = theta[0,0]-np.sum(np.multiply(error, X[:,0])) / len(X)
    
    return np.array(grad).ravel()

#from scipy.optimize import minimize
def one_vs_all(X, y, num_labels, lr):
    rows = X.shape[0]
    params = X.shape[1]
    
     #还是添加偏置bias
    all_theta = np.zeros((num_labels, params + 1))#  shape = (10,401)
    X = np.insert(X, 0, values=np.ones(rows), axis=1)  #shape = (5000,401)
    
    for i in range(1, num_labels + 1):
        theta = np.zeros(params + 1)
        y_i = np.array([1 if label == i else 0 for label in y])
        y_i = np.reshape(y_i, (rows, 1))
        #网上有种方法
        #from scipy.optimize import minimize
        #fmin = minimize(fun=cost, x0=theta, args=(X, y_i, learning_rate), method='TNC', jac=gradient)
        #all_theta[i-1,:] = fmin.x
        #这样预测得更好，但是不容易理解，下面5行容易理解
        for j in range(1000):
            a = gradient(all_theta[i-1,:], X, y_i, lr)
            if(a==all_theta[i-1,:]).all():
                break
            all_theta[i-1,:]=a
    return all_theta

rows = data['X'].shape[0]
params = data['X'].shape[1]

all_theta = np.zeros((10, params + 1))# shape = (10*401)每行对应一种数字的401个weight
#分别在x和theta添加bias
X = np.insert(data['X'], 0, values=np.ones(rows), axis=1)
theta = np.zeros(params + 1)

#y_0 = np.array([1 if label == 0 else 0 for label in data['y']])
#y_0 = np.reshape(y_0, (rows, 1))     这两行没什么用，懂这样做的意义是实现对  数a与非数a的划分 就行 
all_theta = one_vs_all(data['X'], data['y'], 10, 1)
#X.shape=(5000, 401), y_0.shape=(5000, 1), theta.shape=(401,)
def predict_all(X, all_theta):
    rows = X.shape[0]
    params = X.shape[1]
    num_labels = all_theta.shape[0]#   num_labels=10
    #bias
    X = np.insert(X, 0, values=np.ones(rows), axis=1)
    
    X = np.matrix(X)
    all_theta = np.matrix(all_theta)#  shape = (10,401)
    
    h = sigmoid(X * all_theta.T)#计算5000个样本中，每1个样本对应的10种数字的预测概率
    #h_argmax返回最大值的索引
    h_argmax = np.argmax(h, axis=1)#找出每行概率最大值对应的索引
    h_argmax = h_argmax + 1#np的广播机制，每个索引加1，1对应的索引为1，0对应的索引为10
    return h_argmax
#对比结果
y_pred = predict_all(data['X'], all_theta)
print(classification_report(data['y'], y_pred))

task2 神经网络

实现一个可以识别手写数字的神经网络。神经网络可以表示一些非线性复杂的模型。在已经预先训练好基础上，实现前馈神经网络。
输入是图片的像素值，20*20像素的图片有400个输入层单元，不包括需要额外添加的加上常数项。
θ1和θ2已提供,，有25个隐层单元和10个输出单元（10个输出）

weight = loadmat("ex3weights.mat")
theta1, theta2 = weight['Theta1'], weight['Theta2']
theta1.shape, theta2.shape
X2 = np.matrix(np.insert(data['X'], 0, values=np.ones(X.shape[0]), axis=1))
y2 = np.matrix(data['y'])
#X2.shape=(5000, 401), y2.shape=(5000, 1)
a1 = X2
z2 = a1 * theta1.T
#z2.shape=(5000, 25)
a2 = sigmoid(z2)
#a2.shape=(5000, 25)
a2 = np.insert(a2, 0, values=np.ones(a2.shape[0]), axis=1)
z3 = a2 * theta2.T
#z3.shape=(5000, 10)
a3 = sigmoid(z3)
y_pred2 = np.argmax(a3, axis=1) + 1
#y_pred2.shape=(5000, 1)
print(classification_report(y2, y_pred))

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