Perceptron Network __ann

Perceptron Model Analysis

Perceptron Neuron Model

Single-layer Perceptron model:

-"Model total input-" model output

Weighted matrix row number-"Output number"

Weighted matrix column number-"Input number"

Offset matrix row number-number of outputs

Total input y======>>>y<0-"0

y>=0-"1 (0/1 for total output)

Wij is the connection value between the first neuron (the latter layer) and the first J (previous layer) neuron

Perceptual Models for classification

Learning training Algorithm (learning = = = Changing weight)

T: Ideal Output

Training Steps

1 To solve the problem, determine the input vector X, target vector T, so as to determine the dimensions and network structure parameters, n,m;

2) parameter initialization;

3) Set the maximum cycle times;

4 compute the network output;

5) Check the output vector y and the target vector T is the same, if the same, or to reach the maximum number of cycles, training ended, otherwise transferred to 6;

6) Learning

           

and returns 4). Discrete single output perceptron

Training algorithm of discrete single output perceptron

1. Initialization weight vector W, threshold B;

2. Repeat the following process until the training is complete:

2.1 for each sample (X,y), repeat the following procedure:

2.1.1 Input x

2.1.2 Calculation Output o=f (wxt+b);

2.1.3 The weights matrix W and threshold B according to the following formula

w=w+ (y-o) X

b=b+ (Y-o)

discrete multiple output perceptron

Training algorithm of discrete multi-output perceptron

Sample set: {(x,y) | y corresponds to input vector x output}

Input vector: x= (X1,X2,...,XN)

Ideal output vector: y= (Y1,Y2,...,YM)

Activation function: F

Weight Matrix w= (Wij)

Threshold Vector b= (B1,B2,...,BM)

Actual output vector: o= (o1,o2,...,om)

1. Initialization weight matrix W, threshold vector b;

2. Repeat the following process until the training is complete:

2.1 for each sample (X,y), repeat the following procedure:

2.1.1 Input x

2.1.2 Calculation Output o=f (wxt+b);

2.1.3 for I=1 to M performs the following actions:

bi=bi+ (Yi-oi)

For j=1 ton

wij=wij+ (yi-oi) *xj

                                     

continuous multi-output Perceptron training algorithm (* * *)

1. Initialization weight matrix W, threshold vector b;

2. initial Precision control parameter e, learning rate a, precision control variable d= e+1;

3. While D³e do

3.1 d=0;

3.2 for each sample (X,y) do

3.2.1 input x;

3.2.2 Calculation Output o=f (wxt+b);

3.2.3 Modification Weight matrix W and threshold vector B;

3.2.4 Cumulative Error

For i=1to m do

d=d+ (yi-oi) 2

Correction: w[i] = W[i] +α* (Y[i]–t[i]) *p[i];

B[i] = B[i] +α* (y[i]–t[i));

The alpha value is 0~1 decimal, and my alpha value is 0.2. T is the target value.

In order to determine the training effect, here you need to define an error rate, which is defined as an error: E =∑ (Y-T) 2