1. 关于非线性转化方程(non-linear transformation function)
sigmoid函数(S 曲线)用来作为activation function:
1.1 双曲函数(tanh)
1.2 逻辑函数(logistic function)
2. 实现一个简单的神经网络算法
# -*- coding:utf-8 -*-
import numpy as np
def tanh(x):
return np.tanh(x)#双曲函数
def tanh_deriv(x):
return 1.0 - np.tanh(x)*np.tanh(x)#双曲函数的一阶导数
def logistic(x):
return 1/(1 + np.exp(-x))#逻辑函数
def logistic_derivative(x):
return logistic(x)*(1-logistic(x))#逻辑函数的一阶导数
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#[10，2,2] 列表中圆锁的个数对应着一共有几层，数字的值对应着几个神经元，一共三层， 神经元个数分别为 10 2 2 :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):#每次抽取一部分数据训练模型，一次训练就是 1epoch
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):#随机选一个X的实例，对随机网络进行更新
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])))# dot()这是个内积 #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
第二个例子
#!/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 #下载数据的库
from sklearn.metrics import confusion_matrix, classification_report
#这是一个对结果衡量的包，里面有现成的函数
from sklearn.preprocessing import LabelBinarizer
# 对于标称型数据来说，preprocessing.LabelBinarizer是一个很好用的工具。
# 比如可以把yes和no转化为0和1，或是把incident和normal转化为0和1。
# 当然，对于两类以上的标签也是适用的。
from NNdemo1 import NeuralNetwork #我这里的NNdemo1是因为我上一个程序起的名字是NNdemo1.py
from sklearn.model_selection import train_test_split #交叉验证
digits = load_digits()#装载数据集
X = digits.data#特征量
y = digits.target#标签
X -= X.min() # normalize the values to bring them into the range 0-1
X /= X.max() #进行一个简单的预处理，归一化
nn = NeuralNetwork([64, 100, 10], 'logistic')
#层数可以自己定，8*8 = 64个像素点，64个维度，输出层因为要分出0-9所以是9个，隐藏层自己可以灵活点
X_train, X_test, y_train, y_test = train_test_split(X, y)#分测试集和训练集
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)) #通过argmax可以看到第几个数对应最大概率
print confusion_matrix(y_test, predictions)
#y_test测试集真实的标记，prediction我们预测出来的标记，通过这个绘图工具我们就能看出有多少是预测正确的
print classification_report(y_test, predictions)
