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ex4: Back-end propagation neural network
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# Back-end propagation neural network反向傳播神經網絡
# Data set數據集
#MATLAB.m文件，內有5000個20*20的手寫字體圖像，及對應的數字。(數字0的y值，對應的是10)need to use SciPy
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import matplotlib
from scipy.io import loadmat
from sklearn.preprocessing import OneHotEncoder
data = loadmat('Coursera-ML-AndrewNg-Notes-master\\code\\ex4-NN back propagation\\ex4data1.mat')
data
#檢查維度
X = data['X']
y = data['y']
print(X)
X.shape, y.shape
#
weight = loadmat("Coursera-ML-AndrewNg-Notes-master\\code\\ex4-NN back propagation\\ex4weights.mat")
theta1, theta2 = weight['Theta1'], weight['Theta2']
theta1.shape, theta2.shape
# visualization as 100 data
#sharex,sharey：布爾值或者{'none','all','row','col'}，默認：False
#控制x(sharex)或y(sharey)軸之間的屬性共享：
#1.True或者' all'：x或y軸屬性將在所有子圖(subplots)中共享.
#2.False或'none'：每個子圖的x或y軸都是獨立的部分
#3.'row'：每個子圖在一個x或y軸共享行(row)
#4.'col':每個子圖在一個x或y軸共享列(column)
sample_idx = np.random.choice(np.arange(data['X'].shape[0]), 100)
sample_images = data['X'][sample_idx, :]
fig, ax_array = plt.subplots(nrows=10, ncols=10, sharey=True, sharex=True, figsize=(12, 12))
for r in range(10):
for c in range(10):
ax_array[r, c].matshow(np.array(sample_images[10 * r + c].reshape((20, 20))).T,cmap=matplotlib.cm.binary)
plt.xticks(np.array([]))
plt.yticks(np.array([]))
# vectorization and make mult-clasffication as 10 number
# logistic regression's cost function is sigmond function and need to notice it is different to linear regression
def sigmoid(z):
return 1 / (1 + np.exp(-z))
# forward neural
def forward_propagate(X, theta1, theta2):
m = X.shape[0]
a1 = np.insert(X, 0, values=np.ones(m), axis=1)
z2 = a1 * theta1.T
a2 = np.insert(sigmoid(z2), 0, values=np.ones(m), axis=1)
z3 = a2 * theta2.T
h = sigmoid(z3)
return a1, z2, a2, z3, h
# Neural's cost function
def cost(theta1, theta2 , input_size, hidden_size, num_labels, X, y, learning_rate):
m = X.shape[0]
X = np.matrix(X)
y = np.matrix(y)
# run the feed-forward pass
a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)
# compute the cost
J = 0
for i in range(m):
first_term = np.multiply(-y[i,:], np.log(h[i,:]))
second_term = np.multiply((1 - y[i,:]), np.log(1 - h[i,:]))
J += np.sum(first_term - second_term)
J = J / m
return J
# 用Scikitlearn把5000*1 vector變成5000*10的matrix
# encoder = OneHotEncoder(sparse=False)看裡面有幾種不同類別發現有10個將其變矩陣(5000, 10)
encoder = OneHotEncoder(sparse=False)
y_onehot = encoder.fit_transform(y)
y_onehot.shape
y[0], y_onehot[0,:]
# 初始化
input_size = 400
hidden_size = 25
num_labels = 10
learning_rate = 1
cost(theta1, theta2, input_size, hidden_size, num_labels, X, y_onehot, learning_rate)
# Regulation cost function of neural which need plenty theta1 和 theta2
def costReg(theta1, theta2, input_size, hidden_size, num_labels, X, y, learning_rate):
m = X.shape[0]
X = np.matrix(X)
y = np.matrix(y)
# run the feed-forward pass
a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)
# compute the cost
J = 0
for i in range(m):
first_term = np.multiply(-y[i,:], np.log(h[i,:]))
second_term = np.multiply((1 - y[i,:]), np.log(1 - h[i,:]))
J += np.sum(first_term - second_term)
J = J / m
# add the cost regularization term
J += (float(learning_rate) / (2 * m)) * (np.sum(np.power(theta1[:,1:], 2)) + np.sum(np.power(theta2[:,1:], 2)))
return J
costReg(theta1, theta2, input_size, hidden_size, num_labels, X, y_onehot, learning_rate)
# backend property 反向傳播
# still use sigmond function
def sigmoid_gradient(z):
return np.multiply(sigmoid(z), (1 - sigmoid(z)))
# np.random.random(size)有10285個數字將其控制在0.12
params = (np.random.random(size=hidden_size * (input_size + 1) + num_labels * (hidden_size + 1)) - 0.5) * 0.24
#
def backprop(params, input_size, hidden_size, num_labels, X, y, learning_rate):
m = X.shape[0]
X = np.matrix(X)
y = np.matrix(y)
# run the feed-forward pass
a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)
# reshape the parameter array into parameter matrices for each layer
theta1 = np.matrix(np.reshape(params[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))
theta2 = np.matrix(np.reshape(params[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))
# initializations
J = 0
delta1 = np.zeros(theta1.shape) # (25, 401)
delta2 = np.zeros(theta2.shape) # (10, 26)
# compute the cost
for i in range(m):
first_term = np.multiply(-y[i,:], np.log(h[i,:]))
second_term = np.multiply((1 - y[i,:]), np.log(1 - h[i,:]))
J += np.sum(first_term - second_term)
J = J / m
# perform backpropagation
for t in range(m):
a1t = a1[t,:] # (1, 401)
z2t = z2[t,:] # (1, 25)
a2t = a2[t,:] # (1, 26)
ht = h[t,:] # (1, 10)
yt = y[t,:] # (1, 10)
d3t = ht - yt # (1, 10)
z2t = np.insert(z2t, 0, values=np.ones(1)) # (1, 26)
d2t = np.multiply((theta2.T * d3t.T).T, sigmoid_gradient(z2t)) # (1, 26)
delta1 = delta1 + (d2t[:,1:]).T * a1t
delta2 = delta2 + d3t.T * a2t
delta1 = delta1 / m
delta2 = delta2 / m
return J, delta1, delta2
# 梯度校驗 cost plenty time
# Regulation Neural
def backpropReg(params, input_size, hidden_size, num_labels, X, y, learning_rate):
m = X.shape[0]
X = np.matrix(X)
y = np.matrix(y)
# reshape the parameter array into parameter matrices for each layer
theta1 = np.matrix(np.reshape(params[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))
theta2 = np.matrix(np.reshape(params[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))
# run the feed-forward pass
a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)
# initializations
J = 0
delta1 = np.zeros(theta1.shape) # (25, 401)
delta2 = np.zeros(theta2.shape) # (10, 26)
# compute the cost
for i in range(m):
first_term = np.multiply(-y[i,:], np.log(h[i,:]))
second_term = np.multiply((1 - y[i,:]), np.log(1 - h[i,:]))
J += np.sum(first_term - second_term)
J = J / m
# add the cost regularization term
J += (float(learning_rate) / (2 * m)) * (np.sum(np.power(theta1[:,1:], 2)) + np.sum(np.power(theta2[:,1:], 2)))
# perform backpropagation
for t in range(m):
a1t = a1[t,:] # (1, 401)
z2t = z2[t,:] # (1, 25)
a2t = a2[t,:] # (1, 26)
ht = h[t,:] # (1, 10)
yt = y[t,:] # (1, 10)
d3t = ht - yt # (1, 10)
z2t = np.insert(z2t, 0, values=np.ones(1)) # (1, 26)
d2t = np.multiply((theta2.T * d3t.T).T, sigmoid_gradient(z2t)) # (1, 26)
delta1 = delta1 + (d2t[:,1:]).T * a1t
delta2 = delta2 + d3t.T * a2t
delta1 = delta1 / m
delta2 = delta2 / m
# add the gradient regularization term
delta1[:,1:] = delta1[:,1:] + (theta1[:,1:] * learning_rate) / m
delta2[:,1:] = delta2[:,1:] + (theta2[:,1:] * learning_rate) / m
# unravel the gradient matrices into a single array
# numpy.flatten() 與 np.ravel.() 相似
grad = np.concatenate((np.ravel(delta1), np.ravel(delta2)))
return J, grad
# 使用公式解球最憂解
from scipy.optimize import minimize
# minimize the objective function
fmin = minimize(fun=backpropReg, x0=(params), args=(input_size, hidden_size, num_labels, X, y_onehot, learning_rate),
method='TNC', jac=True, options={'maxiter': 250})
fmin
X = np.matrix(X)
thetafinal1 = np.matrix(np.reshape(fmin.x[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))
thetafinal2 = np.matrix(np.reshape(fmin.x[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))
# 把 n帶入function
a1, z2, a2, z3, h = forward_propagate(X, thetafinal1, thetafinal2 )
y_pred = np.array(np.argmax(h, axis=1) + 1)
y_pred
# 預測值與實際值比較
from sklearn.metrics import classification_report #這是評價報告
print(classification_report(y, y_pred))
# visualzation hidden layer 大概25層
hidden_layer = thetafinal1[:, 1:]
hidden_layer.shape
# plot hidden layer
fig, ax_array = plt.subplots(nrows=5, ncols=5, sharey=True, sharex=True, figsize=(12, 12))
for r in range(5):
for c in range(5):
ax_array[r, c].matshow(np.array(hidden_layer[5 * r + c].reshape((20, 20))),cmap=matplotlib.cm.binary)
plt.xticks(np.array([]))
plt.yticks(np.array([]))