理论

机器学习技法：https://www.coursera.org/course/ntumltwo
假设上述网址不可用的话，自行度娘找别人做好的种子。或者看这篇讲义也能够：http://www.cnblogs.com/xbf9xbf/p/4712785.html

Theano代码

须要使用我上一篇博客关于逻辑回归的代码：http://blog.csdn.net/yangnanhai93/article/details/50410026
保存成ls_sgd.py 文件，置于同一个文件夹下就可以。

#!/usr/bin/env python
# -*- encoding:utf-8 -*-
‘‘‘
This is done by Vincent.Y
mainly modified from deep learning tutorial
‘‘‘
import os
import sys
import timeit
import numpy as np
import theano
import theano.tensor as T
from theano import function
from lr_sgd import LogisticRegression ,load_data,plot_decision_boundary
import matplotlib.pyplot as plt
class HiddenLayer():
    def __init__(self,rng,X,n_in,n_out,W=None,b=None,activation=T.tanh):
        self.X=X
        if W is None:
            W_value=http://www.mamicode.com/np.asarray("hljs-number">6.0/(n_in+n_out)),
                    high=np.sqrt(6.0/(n_in+n_out)),
                    size=(n_in,n_out)
                ),
                dtype=theano.config.floatX
            )
            if activation== theano.tensor.nnet.sigmoid:
                W_value*=4

            W=theano.shared(value=http://www.mamicode.com/W_value,name=‘W‘,borrow=True)
        if b is None:
            b_value=http://www.mamicode.com/np.zeros((n_out,),dtype=theano.config.floatX)"hljs-string">‘b‘,borrow=True)

        self.W=W
        self.b=b

        lin_output=T.dot(X,self.W)+self.b
        self.output=(lin_output if activation is None else activation(lin_output))
        self.params=[self.W,self.b]

class MLP():

    def __init__(self,rng,X,n_in,n_hidden,n_out):
        self.hiddenLayer=HiddenLayer(
            rng=rng,
            X=X,
            n_in=n_in,
            n_out=n_hidden,
            activation=T.tanh
        )

        self.logisticRegressionLayer=LogisticRegression(
            X=self.hiddenLayer.output,
            n_in=n_hidden,
            n_out=n_out
        )
        self.L1=(abs(self.hiddenLayer.W).sum()+abs(self.logisticRegressionLayer.W).sum())
        self.L2=((self.hiddenLayer.W**2).sum()+(self.logisticRegressionLayer.W**2).sum())
        self.negative_log_likelihood=self.logisticRegressionLayer.negative_log_likelihood
        self.errors=self.logisticRegressionLayer.errors #this is a function
        self.params=self.logisticRegressionLayer.params+self.hiddenLayer.params
        self.X=X
        self.y_pred=self.logisticRegressionLayer.y_pred


def test_mlp(learning_rate=0.11,L1_reg=0.00,L2_reg=0.0001,n_epochs=6000,n_hidden=10):
    datasets=load_data()
    train_set_x,train_set_y=datasets[0]
    test_set_x,test_set_y=datasets[1]
    x=T.matrix(‘x‘)
    y=T.lvector(‘y‘)
    rng=np.random.RandomState(218)

    classifier=MLP(
        rng=rng,
        X=x,
        n_in=2,
        n_out=2,
        n_hidden=n_hidden
    )

    cost=(classifier.negative_log_likelihood(y)+L1_reg*classifier.L1+L2_reg*classifier.L2)

    test_model=function(
        inputs=[x,y],
        outputs=classifier.errors(y)
    )

    gparams=[T.grad(cost,param) for param in classifier.params]

    updates=[
        (param,param-learning_rate*gparam)
        for param,gparam in zip(classifier.params,gparams)
    ]

    train_model=function(
        inputs=[x,y],
        outputs=cost,
        updates=updates
    )
    epoch=0
    while epoch < n_epochs:
        epoch=epoch+1
        avg_cost=train_model(train_set_x,train_set_y)
        test_cost=test_model(test_set_x,test_set_y)
        print "epoch is %d,train error %f, test error %f"%(epoch,avg_cost,test_cost)
    predict_model=function(
        inputs=[x],
        outputs=classifier.logisticRegressionLayer.y_pred
    )
    plot_decision_boundary(lambda x:predict_model(x),train_set_x,train_set_y)

if __name__=="__main__":
    test_mlp()

效果

迭代600次，隐层数量为2

迭代6000次。隐层数量为20

当隐层数量非常少。如2或者1的时候。添加迭代次数，分类超平面依然是一条直线；当隐层数量多，迭代次数过少的时候分类超平面也是一条直线。所以在训练的过程中。总是要依据训练的结果来调整隐层节点的数量以及迭代次数来获取最好的效果，当中迭代次数可用early stopping来控制。