在人工神经网络领域中，感知机也被指为单层的人工神经网络，以区别于较复杂的多层感知机（Multilayer Perceptron）。 作为一种线性分类器，（单层）感知机可说是最简单的前向人工神经网络形式。尽管结构简单，感知机能够学习并解决相当复杂的问题。感知机主要的本质缺陷是它不能处理线性不可分问题。
感知机使用特征向量来表示的前馈式人工神经网络，它是一种二元分类器，把矩阵上的输入（实数值向量）映射到输出值上（一个二元的值）。
是实数的表式权重的向量，是点积。是偏置，一个常数不依赖于任何输入值。偏置可以认为是激励函数的偏移量，或者给神经元一个基础活跃等级。
(0 或 1)用于对进行分类，看它是肯定的还是否定的，这属于二元分类问题。如果是否定的，那么加权后的输入必须产生一个肯定的值并且大于，这样才能令分类神经元大于阈值0。从空间上看，偏置改变了决策边界的位置（虽然不是定向的）。
由于输入直接经过权重关系转换为输出，所以感知机可以被视为最简单形式的前馈式人工神经网络。
>> P=[0 1 0 1 1;1 1 1 0 0]
P =
0 1 0 1 1
1 1 1 0 0
>>
>> T=[0 1 0 0 0]
T =
0 1 0 0 0
>> net = newp(minmax(P),1)
net =
Neural Network object:
architecture:
numInputs: 1
numLayers: 1
biasConnect: [1]
inputConnect: [1]
layerConnect: [0]
outputConnect: [1]
numOutputs: 1 (read-only)
numInputDelays: 0 (read-only)
numLayerDelays: 0 (read-only)
subobject structures:
inputs: {1x1 cell} of inputs
layers: {1x1 cell} of layers
outputs: {1x1 cell} containing 1 output
biases: {1x1 cell} containing 1 bias
inputWeights: {1x1 cell} containing 1 input weight
layerWeights: {1x1 cell} containing no layer weights
functions:
adaptFcn: 'trains'
divideFcn: (none)
gradientFcn: 'calcgrad'
initFcn: 'initlay'
performFcn: 'mae'
plotFcns: {'plotperform','plottrainstate'}
trainFcn: 'trainc'
parameters:
adaptParam: .passes
divideParam: (none)
gradientParam: (none)
initParam: (none)
performParam: (none)
trainParam: .show, .showWindow, .showCommandLine, .epochs,
.goal, .time
weight and bias values:
IW: {1x1 cell} containing 1 input weight matrix
LW: {1x1 cell} containing no layer weight matrices
b: {1x1 cell} containing 1 bias vector
other:
name: ''
userdata: (user information)
>> net.iw{1,1}
ans =
0 0
>> net.iw{1,1}=[1 1]
net =
Neural Network object:
architecture:
numInputs: 1
numLayers: 1
biasConnect: [1]
inputConnect: [1]
layerConnect: [0]
outputConnect: [1]
numOutputs: 1 (read-only)
numInputDelays: 0 (read-only)
numLayerDelays: 0 (read-only)
subobject structures:
inputs: {1x1 cell} of inputs
layers: {1x1 cell} of layers
outputs: {1x1 cell} containing 1 output
biases: {1x1 cell} containing 1 bias
inputWeights: {1x1 cell} containing 1 input weight
layerWeights: {1x1 cell} containing no layer weights
functions:
adaptFcn: 'trains'
divideFcn: (none)
gradientFcn: 'calcgrad'
initFcn: 'initlay'
performFcn: 'mae'
plotFcns: {'plotperform','plottrainstate'}
trainFcn: 'trainc'
parameters:
adaptParam: .passes
divideParam: (none)
gradientParam: (none)
initParam: (none)
performParam: (none)
trainParam: .show, .showWindow, .showCommandLine, .epochs,
.goal, .time
weight and bias values:
IW: {1x1 cell} containing 1 input weight matrix
LW: {1x1 cell} containing no layer weight matrices
b: {1x1 cell} containing 1 bias vector
other:
name: ''
userdata: (user information)
>> net.b{1}
ans =
0
>> net.b{1}=-2
net =
Neural Network object:
architecture:
numInputs: 1
numLayers: 1
biasConnect: [1]
inputConnect: [1]
layerConnect: [0]
outputConnect: [1]
numOutputs: 1 (read-only)
numInputDelays: 0 (read-only)
numLayerDelays: 0 (read-only)
subobject structures:
inputs: {1x1 cell} of inputs
layers: {1x1 cell} of layers
outputs: {1x1 cell} containing 1 output
biases: {1x1 cell} containing 1 bias
inputWeights: {1x1 cell} containing 1 input weight
layerWeights: {1x1 cell} containing no layer weights
functions:
adaptFcn: 'trains'
divideFcn: (none)
gradientFcn: 'calcgrad'
initFcn: 'initlay'
performFcn: 'mae'
plotFcns: {'plotperform','plottrainstate'}
trainFcn: 'trainc'
parameters:
adaptParam: .passes
divideParam: (none)
gradientParam: (none)
initParam: (none)
performParam: (none)
trainParam: .show, .showWindow, .showCommandLine, .epochs,
.goal, .time
weight and bias values:
IW: {1x1 cell} containing 1 input weight matrix
LW: {1x1 cell} containing no layer weight matrices
b: {1x1 cell} containing 1 bias vector
other:
name: ''
userdata: (user information)
我们这个感知器的任务就是完成 and 运算，即只有输入的2个元素都为 1，输出才为1
sim是仿真函数，对神经网络进行仿真，可以理解为进行测试
>> sim(net,[0;1])
ans =
0
>> sim(net,[1;1])
ans =
1
>> sim(net,[1;0])
ans =
0
>> sim(net,[1;0])
ans =
0
>> y=sim(net,[1;0])
y =
0
mae为计算平均误差,e为误差矩阵，因为人为的设置了正确的权值，所以没有误差,t为正确输出,y为感知机的实际输出
>> y=sim(net,[1 0 1;0 1 1])
y =
0 0 1
>> t=[0 0 1]
t =
0 0 1
>> e=t-y
e =
0 0 0
>> perf=mae(3)
perf =
3
>> perf=mae(e)
perf =
0
>>
注意上面的输入方式是1;0为一组样本，然后0;1为另一组样本，1;1为最后一组样本，共3 组样本，见下面示例
ans(1,1)和ans(2,1)是一组输入数据
>> [1 0 1;0 1 1]
ans =
1 0 1
0 1 1
我们把权值修改成一个错的，来看看误差矩阵和平均误差
>> y=sim(net,[1 0 1;0 1 1])
y =
0 0 0
>> e=t-y
e =
0 0 1
>> perf=mae(e)
perf =
0.3333
>> t
t =
0 0 1
>>
