机器学习算法及代码实现--神经网络

机器学习算法及代码实现–神经网络

1、神经网络

神经网络是一种运算模型，由大量的节点（或称神经元）之间相互联接构成。每个节点代表一种特定的输出函数，称为激励函数（activation function）。每两个节点间的连接都代表一个对于通过该连接信号的加权值，称之为权重，这相当于人工神经网络的记忆。网络的输出则依网络的连接方式，权重值和激励函数的不同而不同。而网络自身通常都是对自然界某种算法或者函数的逼近，也可能是对一种逻辑策略的表达。

2、多层向前神经网络

3、设计神经网络结构

4、反向回馈算法

5、实例

代码

import numpy as np

def tanh(x):
return np.tanh(x)

def tanh_deriv(x):
return 1.0 - np.tanh(x)*np.tanh(x)

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

def logistic_derivative(x):
return logistic(x)*(1-logistic(x))

class NeuralNetwork:
def __init__(self, layers, activation='tanh'):
"""
: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
self.activation_deriv = logistic_derivative
elif activation == 'tanh':
self.activation = tanh
self.activation_deriv = tanh_deriv

self.weights = []
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):
X = np.atleast_2d(X)
temp = np.ones([X.shape[0], X.shape[1]+1])
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])
a = [X[i]]

for l in range(len(self.weights)):  #going forward network, for each layer
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
deltas = [error * self.activation_deriv(a[-1])] #For output layer, Err calculation (delta is updated error)

#Staring backprobagation
for l in range(len(a) - 2, 0, -1): # we need to begin at the second to last layer
#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

简单非线性关系数据集测试(XOR):

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))

手写数字识别：

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.cross_validation 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)