神经网络(BP)算法Python实现及应用

import numpy as np


# 定义tanh函数
def tanh(x):
 return np.tanh(x)


# tanh函数的导数
def tan_deriv(x):
 return 1.0 - np.tanh(x) * np.tan(x)


# sigmoid函数
def logistic(x):
 return 1 / (1 + np.exp(-x))


# sigmoid函数的导数
def logistic_derivative(x):
 return logistic(x) * (1 - logistic(x))


class NeuralNetwork:
 def __init__(self, layers, activation='tanh'):
 """
 神经网络算法构造函数
 :param layers: 神经元层数
 :param activation: 使用的函数（默认tanh函数）
 :return:none
 """
 if activation == 'logistic':
 self.activation = logistic
 self.activation_deriv = logistic_derivative
 elif activation == 'tanh':
 self.activation = tanh
 self.activation_deriv = tan_deriv

 # 权重列表
 self.weights = []
 # 初始化权重（随机）
 for i in range(1, len(layers) - 1):
 self.weights.append((2 * np.random.random((layers[i - 1] + 1, layers[i] + 1)) - 1) * 0.25)
 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
 :param X: 数据集（通常是二维）
 :param y: 分类标记
 :param learning_rate: 学习率（默认0.2）
 :param epochs: 训练次数（最大循环次数，默认10000）
 :return: none
 """
 # 确保数据集是二维的
 X = np.atleast_2d(X)

 temp = np.ones([X.shape[0], X.shape[1] + 1])
 temp[:, 0: -1] = X
 X = temp
 y = np.array(y)

 for k in range(epochs):
 # 随机抽取X的一行
 i = np.random.randint(X.shape[0])
 # 用随机抽取的这一组数据对神经网络更新
 a = [X[i]]
 # 正向更新
 for l in range(len(self.weights)):
 a.append(self.activation(np.dot(a[l], self.weights[l])))
 error = y[i] - a[-1]
 deltas = [error * self.activation_deriv(a[-1])]

 # 反向更新
 for l in range(len(a) - 2, 0, -1):
 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

from NN.NeuralNetwork import NeuralNetwork
import numpy as np

nn = NeuralNetwork([2, 2, 1], 'tanh')
temp = [[0, 0], [0, 1], [1, 0], [1, 1]]
X = np.array(temp)
y = np.array([0, 1, 1, 0])
nn.fit(X, y)
for i in temp:
 print(i, nn.predict(i))

from sklearn.datasets import load_digits
import pylab as pl

digits = load_digits()
print(digits.data.shape)
pl.gray()
pl.matshow(digits.images[0])
pl.show()

import numpy as np
from sklearn.datasets import load_digits
from sklearn.metrics import confusion_matrix, classification_report
from sklearn.preprocessing import LabelBinarizer
from NN.NeuralNetwork import NeuralNetwork
from sklearn.cross_validation import train_test_split

# 加载数据集
digits = load_digits()
X = digits.data
y = digits.target
# 处理数据，使得数据处于0,1之间，满足神经网络算法的要求
X -= X.min()
X /= X.max()

# 层数：
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