在人工神經網絡領域中，感知機也被指為單層的人工神經網絡，以區別于較復雜的多層感知機（Multilayer Perceptron）。 作為一種線性分類器，（單層）感知機可說是最簡單的前向人工神經網絡形式。盡管結構簡單，感知機能夠學習并解決相當復雜的問題。感知機主要的本質缺陷是它不能處理線性不可分問題。

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感知機使用特征向量來表示的前饋式人工神經網絡，它是一種二元分類器，把矩陣上的輸入（實數值向量）映射到輸出值上（一個二元的值）。

是實數的表式權重的向量，是點積。是偏置，一個常數不依賴于任何輸入值。偏置可以認為是激勵函數的偏移量，或者給神經元一個基礎活躍等級。

(0 或 1)用于對進行分類，看它是肯定的還是否定的，這屬于二元分類問題。如果是否定的，那么加權后的輸入必須產生一個肯定的值并且大于，這樣才能令分類神經元大于閾值0。從空間上看，偏置改變了決策邊界的位置（雖然不是定向的）。

由于輸入直接經過權重關系轉換為輸出，所以感知機可以被視為最簡單形式的前饋式人工神經網絡。

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>> 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

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>> 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)

我們這個感知器的任務就是完成 and?運算，即只有輸入的2個元素都為?1，輸出才為1

sim是仿真函數，對神經網絡進行仿真，可以理解為進行測試
>> 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為計算平均誤差,e為誤差矩陣，因為人為的設置了正確的權值，所以沒有誤差,t為正確輸出,y為感知機的實際輸出

>> 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

>>

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注意上面的輸入方式是1;0為一組樣本，然后0;1為另一組樣本，1;1為最后一組樣本，共3 組樣本，見下面示例

ans(1,1)和ans(2,1)是一組輸入數據

>> [1 0 1;0 1 1]

ans =

???? 1???? 0???? 1
???? 0???? 1???? 1

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?我們把權值修改成一個錯的，來看看誤差矩陣和平均誤差

>> 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

>>

matlab-神經網絡-感知器(3)