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前面一篇写了关于简单的字符分离和特征提取，实际上，如果仅仅写个记牌器，那上篇识别出的特征直接用作牌面识别即可，根本无需进一步的工作——利用人工神经网络识别，但毕竟是为了完成前面的网页文章，还是写一下这个网络，因为验证码经处理后，可不会那么“老实”的每次都一模一样，我们需要的是神经网络来识别这些家伙。

从面向对象角度来说，人工神经网络可以向下划分为层，而层是由神经元构成的——神经元是构成人工神经网络的最基本单位，我们应该先实现它。神经元需要接受输入，无论它位于输入层、中间层或是输出层，同样也需要有输出，对于每一个输入，都需要对应一个权值，为了判断这个神经元处于激活还是抑制状态，我们需要一个函数来处理输入从而得到输出——这，就是一个神经元，据此，写出其代码：

Public Class Neuron        '输入个数        Protected m_inputsCount As Integer = 1        '权值        Protected weights As Double() = New Double(0) {}        '激励函数        Protected [function] As IActivationFunction = New SigmoidFunction()        ' 加权的输入和         Protected sum As Double        ' 神经输出值         Protected m_output As Double        '随机数发生器        Protected Shared rand As New Random()        ' 输入总数属性         Public Property InputsCount() As Integer            Get                Return m_inputsCount            End Get            Set(ByVal value As Integer)                m_inputsCount = Math.Max(1, value)                weights = New Double(m_inputsCount - 1) {}            End Set        End Property        ' 激活函数        Public Property ActivationFunction() As IActivationFunction            Get                Return [function]            End Get            Set(ByVal value As IActivationFunction)                [function] = value            End Set        End Property        ' 输出值        Public ReadOnly Property Output() As Double            Get                Return m_output            End Get        End Property        ' 设置—获取权        Default Public Property Item(ByVal index As Integer) As Double            Get                Return weights(index)            End Get            Set(ByVal value As Double)                weights(index) = value            End Set        End Property        ' 创建         Public Sub New()        End Sub        Public Sub New(ByVal inputs As Integer)            Me.New(inputs, New SigmoidFunction())        End Sub        Public Sub New(ByVal inputs As Integer, ByVal [function] As IActivationFunction)            Me.[function] = [function]            InputsCount = inputs        End Sub        ' 计算神经输出值         Public Function Compute(ByVal input As Double()) As Double            If input.Length <> m_inputsCount Then                Throw New ArgumentException()            End If            sum = 0.0            For i As Integer = 0 To m_inputsCount - 1                ' 计算输入值加权和                 sum += weights(i) * input(i)            Next            m_output = [function].Output(sum)            Return m_output        End Function        ' 随机权值         Public Sub Randomize()            For i As Integer = 0 To m_inputsCount - 1                weights(i) = (rand.NextDouble())            Next        End Sub    End Class

这就是一个神经元了。需要解释的是，我们用的S型函数是通过一个接口IActivationFunction来达到“传递”目的的。该接口的

''' 
     ''' 激励函数 —— 接口    ''' 
     Public Interface IActivationFunction        ' 计算函数值        Function Output(ByVal input As Double) As Double        ' 计算函数值微分        Function OutputPrime(ByVal input As Double) As Double        ' 计算函数值微分        ' 使用函数值作为输入        Function OutputPrime2(ByVal input As Double) As Double    End Interface

接下来实现它们即可。

由神经元来构成层，实际上，从某种意义来说，层，也是一个神经，它们的代码极其相似，工作原理也基本相同：

Public Class Layer        ' 输入个数        Protected m_inputsCount As Integer        '神经元个数        Protected m_neuronsCount As Integer        '层激励函数        Protected [function] As IActivationFunction        '神经        Protected neurons As Neuron()        '输出        Protected m_output As Double()        ' 输入个数        Public Property InputsCount() As Integer            Get                Return m_inputsCount            End Get            Set(ByVal value As Integer)                m_inputsCount = Math.Max(1, value)                InitLayer()            End Set        End Property        ' 神经个数        Public Property NeuronsCount() As Integer            Get                Return m_neuronsCount            End Get            Set(ByVal value As Integer)                m_neuronsCount = Math.Max(1, value)                InitLayer()            End Set        End Property        ' 激励函数        Public Property ActivationFunction() As IActivationFunction            Get                Return [function]            End Get            Set(ByVal value As IActivationFunction)                [function] = value                For i As Integer = 0 To m_neuronsCount - 1                    neurons(i).ActivationFunction = value                Next            End Set        End Property        ' 获取指定神经元        Default Public ReadOnly Property Item(ByVal index As Integer) As Neuron            Get                Return neurons(index)            End Get        End Property        ' 获取层输出        Public ReadOnly Property Output() As Double()            Get                Return m_output            End Get        End Property        ' 创建         Public Sub New()            Me.New(1, 1, New SigmoidFunction())        End Sub        Public Sub New(ByVal neuronsCount As Integer)            Me.New(neuronsCount, 1, New SigmoidFunction())        End Sub        Public Sub New(ByVal neuronsCount As Integer, ByVal inputsCount As Integer)            Me.New(neuronsCount, inputsCount, New SigmoidFunction())        End Sub        Public Sub New(ByVal neuronsCount As Integer, ByVal inputsCount As Integer, ByVal [function] As IActivationFunction)            Me.m_inputsCount = Math.Max(1, inputsCount)            Me.m_neuronsCount = Math.Max(1, neuronsCount)            Me.[function] = [function]            InitLayer()        End Sub        ' 计算层输出        Public Function Compute(ByVal input As Double()) As Double()            For i As Integer = 0 To m_neuronsCount - 1                m_output(i) = neurons(i).Compute(input)            Next            Return m_output        End Function        ' 随机化该层        Public Sub Randomize()            For Each neuron As Neuron In neurons                neuron.Randomize()            Next        End Sub        ' 初始化层        Private Sub InitLayer()            ' 创建层            neurons = New Neuron(m_neuronsCount - 1) {}            For i As Integer = 0 To m_neuronsCount - 1                neurons(i) = New Neuron(m_inputsCount, [function])            Next            ' 分配输出数组            m_output = New Double(m_neuronsCount - 1) {}        End Sub    End Class

只是层里面的激励函数我们另外实现，当然，用S型函数也不是不可以。。。。

接下来就是由层构成网络，还是上面那句话，网络啊，工作原理也和神经有点类似，代码基本是重复的罗列：

    ''' 
     ''' 网络——神经层的集合     ''' 
     
   
     Public Class Network        ' 输入个数        Protected inputsCount As Integer        '层数        Protected m_layersCount As Integer        '输出        Protected m_output As Double()        '层        Protected layers As Layer()
   

        ' 层数        Public ReadOnly Property LayersCount() As Integer            Get                Return m_layersCount            End Get        End Property        ' 获取指定层        Default Public ReadOnly Property Item(ByVal index As Integer) As Layer            Get                Return layers(index)            End Get        End Property        ' 获取输出         Public ReadOnly Property Output() As Double()            Get                Return m_output            End Get        End Property        Sub New()        End Sub        ' Constructors         Public Sub New(ByVal inputsCount As Integer, ByVal ParamArray neuronsCountPerLayer As Integer())            Me.New(New SigmoidFunction(), inputsCount, neuronsCountPerLayer)        End Sub        Public Sub New(ByVal [function] As IActivationFunction, ByVal inputsCount As Integer, ByVal ParamArray neuronsCountPerLayer As Integer())            Me.inputsCount = Math.Max(1, inputsCount)            Me.m_layersCount = neuronsCountPerLayer.Length            ' 创建层集合            layers = New Layer(m_layersCount - 1) {}            For i As Integer = 0 To m_layersCount - 1                Dim m As Integer = 0                If i = 0 Then m = inputsCount Else m = neuronsCountPerLayer(i - 1)                layers(i) = New Layer(neuronsCountPerLayer(i), m, [function])            Next        End Sub

        ' 计算输出        Public Function Compute(ByVal input As Double()) As Double()            m_output = input            For i As Integer = 0 To m_layersCount - 1                m_output = layers(i).Compute(m_output)            Next            Return m_output        End Function

        ' 随机化网络        Public Sub Randomize()            For Each layer As Layer In layers                layer.Randomize()            Next        End Sub

    End Class

如此，就构成了这个神经网络。。。。。。

具体应用呢，我们需要另外定义一些属性、方法，来实现Back Propagation Learning：

属性：

1、学习速率

2、精度

3、动量

方法：

1、学习

2、计算误差

3、更新数据（各层权值直至各神经权值）

代码就是一些循环，不贴了。

有一点需要注意的，就是从图像中提取适当个数的特征可以加速学习和识别速度，但是太少就会影响网络的判断能力。

结合前面例子，我们可以提取垂直投影特征，来解决那些最幼稚的验证码：）有兴趣的话可以实现下。

一下是针对某网站的验证码图片处理后得到的一组学习图片采用随机特征提取后（图片大小14*18，提取特征40个，学习精度0.01），进行学习的数据：

学习次数     误差       Now.Second（当前时间的秒）

100  1.74766228723842   49200  1.33293174843217   49300  1.21399094064815   49400  1.15740689778003   49500  1.12433264177344   49600  1.10263310876503   50700  1.08728586760529   50800  1.07582728337775   50900  1.06688719120981   501000  1.05958542167266   501100  1.05308338562932   511200  1.04373940177007   511247  0.997537607633144   511300  0.608558811884911   511400  0.304230610883604   511500  0.212165790693552   511600  0.165892333507009   511700  0.138465048204805   521800  0.120396685718836   521900  0.107594382540998   521978  0.099921549727966   52

从上面数据可以看出，如果特征提取位置较好（这里是随机生成），则学习速度很快，几秒时间即可学习完成。

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