神经网络一（Neural Network）
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import numpy as np#矩阵运算
def tanh(x):
return np.tanh(x)
def tanh_deriv(x):#对tanh求导
return 1.0 - np.tanh(x)*np.tanh(x)
def logistic(x):#s函数
return 1/(1 + np.exp(-x))
def logistic_derivative(x):#对s函数求导
return logistic(x)*(1-logistic(x))
class NeuralNetwork:#面向对象定义一个神经网络类
def __init__(self, layers, activation='tanh'):#下划线构造函数self 相当于本身这个类的指针 layer就是一个list 数字代表神经元个数
"""
:param layers: A list containing the number of units in each layer.
Should be at least two values
:param activation: The activation function to be used. Can be
"logistic" or "tanh"
"""
if activation == 'logistic':
self.activation = logistic#之前定义的s函数
self.activation_deriv = logistic_derivative#求导函数
elif activation == 'tanh':
self.activation = tanh#双曲线函数
self.activation_deriv = tanh_deriv#求导双曲线函数
self.weights = []#初始化一个list作为 权重
#初始化权重两个值之间随机初始化
for i in range(1, len(layers) - 1):#有几层神经网络 除去输出层
#i-1层 和i层之间的权重 随机生成layers[i - 1] + 1 * layers[i] + 1 的矩阵 -0.25-0.25
self.weights.append((2*np.random.random((layers[i - 1] + 1, layers[i] + 1))-1)*0.25)
#i层和i+1层之间的权重
self.weights.append((2*np.random.random((layers[i] + 1, layers[i + 1]))-1)*0.25)
def fit(self, X, y, learning_rate=0.2, epochs=10000):#训练神经网络
#learning rate
X = np.atleast_2d(X)#x至少2维
temp = np.ones([X.shape[0], X.shape[1]+1])#初始化一个全为1的矩阵
temp[:, 0:-1] = X # adding the bias unit to the input layer
X = temp
y = np.array(y)
for k in range(epochs):
i = np.random.randint(X.shape[0])#随机选行
a = [X[i]]
for l in range(len(self.weights)): #going forward network, for each layer
#选择一条实例与权重点乘 并且将值传给激活函数，经过a的append 使得所有神经元都有了值（正向）
a.append(self.activation(np.dot(a[l], self.weights[l]))) #Computer the node value for each layer (O_i) using activation function
error = y[i] - a[-1] #Computer the error at the top layer 真实值与计算值的差（向量）
#通过求导 得到权重应当调整的误差
deltas = [error * self.activation_deriv(a[-1])] #For output layer, Err calculation (delta is updated error)
#Staring backprobagation 更新weight
for l in range(len(a) - 2, 0, -1): # we need to begin at the second to last layer 每次减一
#Compute the updated error (i,e, deltas) for each node going from top layer to input layer
deltas.append(deltas[-1].dot(self.weights[l].T)*self.activation_deriv(a[l]))
deltas.reverse()
for i in range(len(self.weights)):
layer = np.atleast_2d(a[i])
delta = np.atleast_2d(deltas[i])
self.weights[i] += learning_rate * layer.T.dot(delta)
def predict(self, x):
x = np.array(x)
temp = np.ones(x.shape[0]+1)
temp[0:-1] = x
a = temp
for l in range(0, len(self.weights)):
a = self.activation(np.dot(a, self.weights[l]))
return a
异或运算
from NeuralNetwork import NeuralNetwork
import numpy as np
nn = NeuralNetwork([2, 2, 1], 'tanh')
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([0, 1, 1, 0])
nn.fit(X, y)
for i in [[0, 0], [0, 1], [1, 0], [1, 1]]:
print(i, nn.predict(i))
([0, 0], array([-0.00475208])) ([0, 1], array([ 0.99828477])) ([1, 0], array([ 0.99827186])) ([1, 1], array([-0.00776711]))
手写体识别
#!/usr/bin/python
# -*- coding:utf-8 -*-
# 每个图片8x8 识别数字：0,1,2,3,4,5,6,7,8,9
import numpy as np
from sklearn.datasets import load_digits
from sklearn.metrics import confusion_matrix, classification_report
from sklearn.preprocessing import LabelBinarizer
from NeuralNetwork import NeuralNetwork
from sklearn.model_selection import train_test_split
digits = load_digits()
X = digits.data
y = digits.target
X -= X.min() # normalize the values to bring them into the range 0-1
X /= X.max()
nn = NeuralNetwork([64, 100, 10], 'logistic')
X_train, X_test, y_train, y_test = train_test_split(X, y)
labels_train = LabelBinarizer().fit_transform(y_train)
labels_test = LabelBinarizer().fit_transform(y_test)
print "start fitting"
nn.fit(X_train, labels_train, epochs=3000)
predictions = []
for i in range(X_test.shape[0]):
o = nn.predict(X_test[i])
predictions.append(np.argmax(o))
print confusion_matrix(y_test, predictions)
print classification_report(y_test, predictions)
confusion_matrix
precision recall f1-score support
0 1.00 0.97 0.99 34
1 0.75 0.91 0.82 46
2 1.00 0.92 0.96 50
3 1.00 0.92 0.96 51
4 0.94 0.91 0.92 53
5 0.95 0.96 0.96 57
6 0.97 0.95 0.96 38
7 0.88 1.00 0.93 35
8 0.88 0.83 0.85 42
9 0.86 0.82 0.84 44
avg / total 0.92 0.92 0.92 450
