Perceptron: Difference between revisions
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show=wordpos(run,'0 1' tries)>0 |
show=wordpos(run,'0 1' tries)>0 |
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If run>0 Then Say ' ' |
If run>0 Then Say ' ' |
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If show Then Say 'Point x f(x) r y |
If show Then Say 'Point x f(x) r y ff ok zz' |
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zz=0 |
zz=0 |
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Do d=1 To dots |
Do d=1 To dots |
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Return</lang> |
Return</lang> |
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{{out}} |
{{out}} |
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<pre>Point x f(x) r y |
<pre>Point x f(x) r y ff ok zz |
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1 100 110 < 204 1 ok 1 |
1 100 110 < 204 1 ok 1 |
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2 613 469 > 117 1 -- 1 |
2 613 469 > 117 1 -- 1 |
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Initial pattern 7 points fire. weights= 0.28732 0.50931 0.45298 |
Initial pattern 7 points fire. weights= 0.28732 0.50931 0.45298 |
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Point x f(x) r y |
Point x f(x) r y ff ok zz |
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1 100 110 < 204 1 ok 1 |
1 100 110 < 204 1 ok 1 |
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2 613 469 > 117 1 -- 1 |
2 613 469 > 117 1 -- 1 |
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After 9 loops 29 points fire. weights=-0.21601 0.29294 0.45176 |
After 9 loops 29 points fire. weights=-0.21601 0.29294 0.45176 |
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Point x f(x) r y |
Point x f(x) r y ff ok zz |
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1 100 110 < 204 1 ok 1 |
1 100 110 < 204 1 ok 1 |
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2 613 469 > 117 -1 ok 2 |
2 613 469 > 117 -1 ok 2 |
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--------------------------------- |
--------------------------------- |
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After 10 loops 29 points fire. weights=-0.21883 0.29057 0.45174</pre> |
After 10 loops 29 points fire. weights=-0.21883 0.29057 0.45174</pre> |
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=={{header|Scala}}== |
=={{header|Scala}}== |
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Revision as of 15:28, 21 October 2018
Perceptron is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
A perceptron is an algorithm used in machine-learning. It's the simplest of all neural networks, consisting of only one neuron, and is typically used for pattern recognition.
A perceptron attempts to separate input into a positive and a negative class with the aid of a linear function. The inputs are each multiplied by weights, random weights at first, and then summed. Based on the sign of the sum a decision is made.
In order for the perceptron to make the right decision, it needs to train with input for which the correct outcome is known, so that the weights can slowly be adjusted until they start producing the desired results.
- Task
The website The Nature of Code demonstrates a perceptron by making it perform a very simple task : determine if a randomly chosen point (x, y) is above or below a line:
y = mx + b
Implement this perceptron and display an image (or some other visualization) of the result.
- See also
Go
This is based on the Java entry but just outputs the final image (as a .png file) rather than displaying its gradual build up. It also uses a different color scheme - blue and red circles with a black dividing line.
<lang go>package main
import (
"github.com/fogleman/gg" "math/rand" "time"
)
const c = 0.00001
func linear(x float64) float64 {
return x*0.7 + 40
}
type trainer struct {
inputs []float64 answer int
}
func newTrainer(x, y float64, a int) *trainer {
return &trainer{[]float64{x, y, 1}, a}
}
type perceptron struct {
weights []float64 training []*trainer
}
func newPerceptron(n, w, h int) *perceptron {
weights := make([]float64, n)
for i := 0; i < n; i++ {
weights[i] = rand.Float64()*2 - 1
}
training := make([]*trainer, 2000)
for i := 0; i < 2000; i++ {
x := rand.Float64() * float64(w)
y := rand.Float64() * float64(h)
answer := 1
if y < linear(x) {
answer = -1
}
training[i] = newTrainer(x, y, answer)
}
return &perceptron{weights, training}
}
func (p *perceptron) feedForward(inputs []float64) int {
if len(inputs) != len(p.weights) {
panic("weights and input length mismatch, program terminated")
}
sum := 0.0
for i, w := range p.weights {
sum += inputs[i] * w
}
if sum > 0 {
return 1
}
return -1
}
func (p *perceptron) train(inputs []float64, desired int) {
guess := p.feedForward(inputs)
err := float64(desired - guess)
for i := range p.weights {
p.weights[i] += c * err * inputs[i]
}
}
func (p *perceptron) draw(dc *gg.Context, iterations int) {
le := len(p.training)
for i, count := 0, 0; i < iterations; i, count = i+1, (count+1)%le {
p.train(p.training[count].inputs, p.training[count].answer)
}
x := float64(dc.Width())
y := linear(x)
dc.SetLineWidth(2)
dc.SetRGB255(0, 0, 0) // black line
dc.DrawLine(0, linear(0), x, y)
dc.Stroke()
dc.SetLineWidth(1)
for i := 0; i < le; i++ {
guess := p.feedForward(p.training[i].inputs)
x := p.training[i].inputs[0] - 4
y := p.training[i].inputs[1] - 4
if guess > 0 {
dc.SetRGB(0, 0, 1) // blue circle
} else {
dc.SetRGB(1, 0, 0) // red circle
}
dc.DrawCircle(x, y, 8)
dc.Stroke()
}
}
func main() {
rand.Seed(time.Now().UnixNano())
w, h := 640, 360
perc := newPerceptron(3, w, h)
dc := gg.NewContext(w, h)
dc.SetRGB(1, 1, 1) // white background
dc.Clear()
perc.draw(dc, 2000)
dc.SavePNG("perceptron.png")
}</lang>
Java
<lang java>import java.awt.*; import java.awt.event.ActionEvent; import java.util.*; import javax.swing.*; import javax.swing.Timer;
public class Perceptron extends JPanel {
class Trainer {
double[] inputs;
int answer;
Trainer(double x, double y, int a) {
inputs = new double[]{x, y, 1};
answer = a;
}
}
Trainer[] training = new Trainer[2000]; double[] weights; double c = 0.00001; int count;
public Perceptron(int n) {
Random r = new Random();
Dimension dim = new Dimension(640, 360);
setPreferredSize(dim);
setBackground(Color.white);
weights = new double[n];
for (int i = 0; i < weights.length; i++) {
weights[i] = r.nextDouble() * 2 - 1;
}
for (int i = 0; i < training.length; i++) {
double x = r.nextDouble() * dim.width;
double y = r.nextDouble() * dim.height;
int answer = y < f(x) ? -1 : 1;
training[i] = new Trainer(x, y, answer);
}
new Timer(10, (ActionEvent e) -> {
repaint();
}).start();
}
private double f(double x) {
return x * 0.7 + 40;
}
int feedForward(double[] inputs) {
assert inputs.length == weights.length : "weights and input length mismatch";
double sum = 0;
for (int i = 0; i < weights.length; i++) {
sum += inputs[i] * weights[i];
}
return activate(sum);
}
int activate(double s) {
return s > 0 ? 1 : -1;
}
void train(double[] inputs, int desired) {
int guess = feedForward(inputs);
double error = desired - guess;
for (int i = 0; i < weights.length; i++) {
weights[i] += c * error * inputs[i];
}
}
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
// we're drawing upside down
int x = getWidth();
int y = (int) f(x);
g.setStroke(new BasicStroke(2));
g.setColor(Color.orange);
g.drawLine(0, (int) f(0), x, y);
train(training[count].inputs, training[count].answer);
count = (count + 1) % training.length;
g.setStroke(new BasicStroke(1));
g.setColor(Color.black);
for (int i = 0; i < count; i++) {
int guess = feedForward(training[i].inputs);
x = (int) training[i].inputs[0] - 4;
y = (int) training[i].inputs[1] - 4;
if (guess > 0)
g.drawOval(x, y, 8, 8);
else
g.fillOval(x, y, 8, 8);
}
}
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Perceptron");
f.setResizable(false);
f.add(new Perceptron(3), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}</lang>
JavaScript
Uses P5 lib. <lang javascript> const EPOCH = 1500, TRAINING = 1, TRANSITION = 2, SHOW = 3;
var perceptron; var counter = 0; var learnRate = 0.02; var state = TRAINING;
function setup() {
createCanvas( 800, 600 ); clearBack(); perceptron = new Perceptron( 2 );
}
function draw() {
switch( state ) {
case TRAINING: training(); break;
case TRANSITION: transition(); break;
case SHOW: show(); break;
}
}
function clearBack() {
background( 0 ); stroke( 255 ); strokeWeight( 4 );
var x = width; line( 0, 0, x, lineDef( x ) );
}
function transition() {
clearBack(); state = SHOW;
}
function lineDef( x ) {
return .75 * x;
}
function training() {
var a = random( width ),
b = random( height );
lDef = lineDef( a ) > b ? -1 : 1;
perceptron.setInput( [a, b] ); perceptron.feedForward(); var pRes = perceptron.getOutput(); var match = (pRes == lDef); var clr;
if( !match ) {
var err = ( pRes - lDef ) * learnRate;
perceptron.adjustWeights( err );
clr = color( 255, 0, 0 );
} else {
clr = color( 0, 255, 0 );
}
noStroke(); fill( clr ); ellipse( a, b, 4, 4 );
if( ++counter == EPOCH ) state = TRANSITION;
}
function show() {
var a = random( width ),
b = random( height ),
clr;
perceptron.setInput( [a, b] ); perceptron.feedForward(); var pRes = perceptron.getOutput();
if( pRes < 0 )
clr = color( 255, 0, 0 );
else
clr = color( 0, 255, 0 );
noStroke(); fill( clr ); ellipse( a, b, 4, 4 );
}
function Perceptron( inNumber ) {
this.inputs = [];
this.weights = [];
this.output;
this.bias = 1;
// one more weight for bias
for( var i = 0; i < inNumber + 1; i++ ) {
this.weights.push( Math.random() );
};
this.activation = function( a ) {
return( Math.tanh( a ) < .5 ? 1 : -1 );
}
this.feedForward = function() {
var sum = 0;
for( var i = 0; i < this.inputs.length; i++ ) {
sum += this.inputs[i] * this.weights[i];
}
sum += this.bias * this.weights[this.weights.length - 1];
this.output = this.activation( sum ); }
this.getOutput = function() {
return this.output;
}
this.setInput= function( inputs ) {
this.inputs = [];
for( var i = 0; i < inputs.length; i++ ) {
this.inputs.push( inputs[i] );
}
}
this.adjustWeights = function( err ) {
for( var i = 0; i < this.weights.length - 1; i++ ) {
this.weights[i] += err * this.inputs[i];
}
}
} </lang> File:PerceptronJS.png
Well, it seems I cannot upload an image :(
Kotlin
<lang scala>// version 1.1.4-3
import java.awt.* import java.awt.event.ActionEvent import java.util.Random import javax.swing.JPanel import javax.swing.JFrame import javax.swing.Timer import javax.swing.SwingUtilities
class Perceptron(n: Int) : JPanel() {
class Trainer(x: Double, y: Double, val answer: Int) {
val inputs = doubleArrayOf(x, y, 1.0)
}
val weights: DoubleArray val training: Array<Trainer> val c = 0.00001 var count = 0
init {
val r = Random()
val dim = Dimension(640, 360)
preferredSize = dim
background = Color.white
weights = DoubleArray(n) { r.nextDouble() * 2.0 - 1.0 }
training = Array(2000) {
val x = r.nextDouble() * dim.width
val y = r.nextDouble() * dim.height
val answer = if (y < f(x)) -1 else 1
Trainer(x, y, answer)
}
Timer(10) { repaint() }.start()
}
private fun f(x: Double) = x * 0.7 + 40.0
fun feedForward(inputs: DoubleArray): Int {
if (inputs.size != weights.size)
throw IllegalArgumentException("Weights and input length mismatch")
val sum = weights.zip(inputs) { w, i -> w * i }.sum()
return activate(sum)
}
fun activate(s: Double) = if (s > 0.0) 1 else -1
fun train(inputs: DoubleArray, desired: Int) {
val guess = feedForward(inputs)
val error = desired - guess
for (i in 0 until weights.size) weights[i] += c * error * inputs[i]
}
public override fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON)
// we're drawing upside down
var x = width
var y = f(x.toDouble()).toInt()
g.stroke = BasicStroke(2.0f)
g.color = Color.orange
g.drawLine(0, f(0.0).toInt(), x, y)
train(training[count].inputs, training[count].answer)
count = (count + 1) % training.size
g.stroke = BasicStroke(1.0f)
g.color = Color.black
for (i in 0 until count) {
val guess = feedForward(training[i].inputs)
x = training[i].inputs[0].toInt() - 4
y = training[i].inputs[1].toInt() - 4
if (guess > 0) g.drawOval(x, y, 8, 8)
else g.fillOval(x, y, 8, 8)
}
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
with(f) {
defaultCloseOperation = JFrame.EXIT_ON_CLOSE
title = "Perceptron"
isResizable = false
add(Perceptron(3), BorderLayout.CENTER)
pack()
setLocationRelativeTo(null)
isVisible = true
}
}
}</lang>
Lua
Simple implementation allowing for any number of inputs (in this case, just 1), testing of the Perceptron, and training. <lang lua>local Perceptron = {} Perceptron.__index = Perceptron
function Perceptron.new(numInputs)
local cell = {}
setmetatable(cell, Perceptron)
cell.weights = {}
cell.bias = math.random()
cell.output = 0
for i = 1, numInputs do
cell.weights[i] = math.random()
end
return cell
end
--used in both training and testing, calculates the output from inputs and weights function Perceptron:update(inputs)
local sum = self.bias
for i = 1, #inputs do
sum = sum + self.weights[i] * inputs[i]
end
self.output = sum
end
--returns the output from a given table of inputs function Perceptron:test(inputs)
self:update(inputs) return self.output
end
--used in training to adjust the weights and bias function Perceptron:optimize(stepSize)
local gradient = self.delta * self.output
for i = 1, #self.weights do
self.weights[i] = self.weights[i] + (stepSize*gradient)
end
self.bias = self.bias + (stepSize*self.delta)
end
--takes a table of training data, the number of iterations (or epochs) to train over, and the step size for training function Perceptron:train(data, iterations, stepSize)
for i = 1, iterations do
for j = 1, #data do
local datum = data[j]
self:update(datum[1])
self.delta = datum[2] - self.output
self:optimize(stepSize)
end
end
end
local node = Perceptron.new(1) --creates a new Perceptron that takes in 1 input local trainingData = {} --this Perceptron will be trained on the function y=2x+1 print("Untrained results:") for i = -2, 2, 1 do
print(i..":", node:test({i}))
trainingData[i+3] = {{i},2*i+1} --the training data is a table, where each element is another table that has a table of inputs and one output
end node:train(trainingData, 100, .1) --trains on the set for 100 epochs with a step size of 0.1 print("\nTrained results:") for i = -2, 2, 1 do
print(i..":", node:test({i}))
end </lang>
- Output:
Untrained results: -2: -0.55767321178784 -1: 0.1898736124016 0: 0.93742043659104 1: 1.6849672607805 2: 2.4325140849699 Trained results: -2: -3 -1: -1 0: 1 1: 3 2: 5
Pascal
This is a text-based implementation, using a 20x20 grid (just like the original Mark 1 Perceptron had). The rate of improvement drops quite markedly as you increase the number of training runs. <lang pascal>program Perceptron;
(*
* implements a version of the algorithm set out at * http://natureofcode.com/book/chapter-10-neural-networks/ , * but without graphics *)
function targetOutput( a, b : integer ) : integer; (* the function the perceptron will be learning is f(x) = 2x + 1 *) begin
if a * 2 + 1 < b then
targetOutput := 1
else
targetOutput := -1
end;
procedure showTargetOutput; var x, y : integer; begin
for y := 10 downto -9 do
begin
for x := -9 to 10 do
if targetOutput( x, y ) = 1 then
write( '#' )
else
write( 'O' );
writeln
end;
writeln
end;
procedure randomWeights( var ws : array of real ); (* start with random weights -- NB pass by reference *) var i : integer; begin
randomize; (* seed random-number generator *)
for i := 0 to 2 do
ws[i] := random * 2 - 1
end;
function feedForward( ins : array of integer; ws : array of real ) : integer; (* the perceptron outputs 1 if the sum of its inputs multiplied by its input weights is positive, otherwise -1 *) var sum : real;
i : integer;
begin
sum := 0;
for i := 0 to 2 do
sum := sum + ins[i] * ws[i];
if sum > 0 then
feedForward := 1
else
feedForward := -1
end;
procedure showOutput( ws : array of real ); var inputs : array[0..2] of integer;
x, y : integer;
begin
inputs[2] := 1; (* bias *)
for y := 10 downto -9 do
begin
for x := -9 to 10 do
begin
inputs[0] := x;
inputs[1] := y;
if feedForward( inputs, ws ) = 1 then
write( '#' )
else
write( 'O' )
end;
writeln
end;
writeln
end;
procedure train( var ws : array of real; runs : integer ); (* pass the array of weights by reference so it can be modified *) var inputs : array[0..2] of integer;
error : real; x, y, i, j : integer;
begin
inputs[2] := 1; (* bias *)
for i := 1 to runs do
begin
for y := 10 downto -9 do
begin
for x := -9 to 10 do
begin
inputs[0] := x;
inputs[1] := y;
error := targetOutput( x, y ) - feedForward( inputs, ws );
for j := 0 to 2 do
ws[j] := ws[j] + error * inputs[j] * 0.01;
(* 0.01 is the learning constant *)
end;
end;
end;
end;
var weights : array[0..2] of real;
begin
writeln( 'Target output for the function f(x) = 2x + 1:' ); showTargetOutput; randomWeights( weights ); writeln( 'Output from untrained perceptron:' ); showOutput( weights ); train( weights, 1 ); writeln( 'Output from perceptron after 1 training run:' ); showOutput( weights ); train( weights, 4 ); writeln( 'Output from perceptron after 5 training runs:' ); showOutput( weights )
end.</lang>
- Output:
Target output for the function f(x) = 2x + 1: ##############OOOOOO #############OOOOOOO #############OOOOOOO ############OOOOOOOO ############OOOOOOOO ###########OOOOOOOOO ###########OOOOOOOOO ##########OOOOOOOOOO ##########OOOOOOOOOO #########OOOOOOOOOOO #########OOOOOOOOOOO ########OOOOOOOOOOOO ########OOOOOOOOOOOO #######OOOOOOOOOOOOO #######OOOOOOOOOOOOO ######OOOOOOOOOOOOOO ######OOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO ####OOOOOOOOOOOOOOOO Output from untrained perceptron: OOO################# OOOO################ OOOOO############### OOOOO############### OOOOOO############## OOOOOO############## OOOOOOO############# OOOOOOOO############ OOOOOOOO############ OOOOOOOOO########### OOOOOOOOO########### OOOOOOOOOO########## OOOOOOOOOOO######### OOOOOOOOOOO######### OOOOOOOOOOOO######## OOOOOOOOOOOOO####### OOOOOOOOOOOOO####### OOOOOOOOOOOOOO###### OOOOOOOOOOOOOO###### OOOOOOOOOOOOOOO##### Output from perceptron after 1 training run: ###############OOOOO ###############OOOOO ##############OOOOOO #############OOOOOOO #############OOOOOOO ############OOOOOOOO ############OOOOOOOO ###########OOOOOOOOO ##########OOOOOOOOOO ##########OOOOOOOOOO #########OOOOOOOOOOO #########OOOOOOOOOOO ########OOOOOOOOOOOO #######OOOOOOOOOOOOO #######OOOOOOOOOOOOO ######OOOOOOOOOOOOOO ######OOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO ####OOOOOOOOOOOOOOOO ####OOOOOOOOOOOOOOOO Output from perceptron after 5 training runs: ##############OOOOOO #############OOOOOOO #############OOOOOOO ############OOOOOOOO ############OOOOOOOO ###########OOOOOOOOO ###########OOOOOOOOO ##########OOOOOOOOOO ##########OOOOOOOOOO #########OOOOOOOOOOO #########OOOOOOOOOOO ########OOOOOOOOOOOO ########OOOOOOOOOOOO #######OOOOOOOOOOOOO #######OOOOOOOOOOOOO ######OOOOOOOOOOOOOO ######OOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO ####OOOOOOOOOOOOOOOO
Racket
<lang racket>#lang racket (require 2htdp/universe
2htdp/image)
(define (activate s) (if (positive? s) 1 -1))
- ---------------------------------------------------------------------------------------------------
- PERCEPTRON
(define perceptron%
(class object% (super-new) (init-field n) (field [weights (build-vector n (λ (i) (- (* (random) 2) 1)))]) (define c 0.001)
(define/public (feed-forward inputs)
(unless (= (vector-length inputs) (vector-length weights))
(error 'feed-forward "weights and inputs lengths mismatch"))
(activate (for/sum ((i (in-vector inputs)) (w (in-vector weights))) (* i w))))
(define/public (train! inputs desired)
(let ((error (- desired (feed-forward inputs))))
(set! weights (vector-map (λ (w i) (+ w (* c error i))) weights inputs))))))
- ---------------------------------------------------------------------------------------------------
- TRAINING
(struct training-data (inputs answer))
(define (make-training-data x y f)
(training-data (vector x y 1) (activate (- (f x) y))))
- ---------------------------------------------------------------------------------------------------
- DEMO
(define (demo)
(struct demonstration (p w h f i))
(define (draw-classification-space p w h scl n)
(for/fold ((scn (place-image (text (~a (get-field weights p)) 12 "red")
(* scl (/ w 2))
(* scl (/ h 2))
(empty-scene (* w scl) (* h scl)))))
((_ (in-range n)))
(let* ((x (* (random) w))
(y (* (random) h))
(guess+? (positive? (send p feed-forward (vector x y 1)))))
(place-image (rectangle 4 4 (if guess+? 'solid 'outline) (if guess+? 'red 'black))
(- (* scl x) 2) (- (* scl (- h y)) 2)
scn))))
(define the-demo
(let ((w 640/100) (h 360/100) (f (λ (x) (+ (* x 0.7) 0.8))))
(demonstration (new perceptron% [n 3]) w h f 0)))
(define (demo-train p w h f)
(let ((td (make-training-data (* (random) w) (* (random) h) f)))
(send p train! (training-data-inputs td) (training-data-answer td))))
(define tick-handler
(match-lambda
[(and d (demonstration p w h f i))
(for ((_ (in-range 100))) (demo-train p w h f))
(struct-copy demonstration d [i (+ 100 i)])]))
(define draw-demo (match-lambda
[(demonstration p w h f i)
(let ((scl 100))
(scene+line (place-image (text (~a i) 24 "magenta")
(* scl (/ w 2))
(* scl (/ h 3))
(draw-classification-space p w h scl 1000))
0 (* scl (- h (f 0))) (* scl w) (* scl (- h (f w))) "red"))]))
(big-bang the-demo (to-draw draw-demo) (on-tick tick-handler)))
(module+ main (demo))</lang>
Run it and see the image for yourself, I can't get it onto RC!
REXX
<lang rexx>/* REXX */ Call init Call time 'R' try=0 Call show 0 Do d=1 To dots
x=x.d y=y.d Parse Value x y 1 with inputs.0 inputs.1 inputs.2 answer.d=sign(y-f(x)) Select When f(x)<y Then r='<' When f(x)>y Then r='>' Otherwise r='=' End training.d=x y 1 answer.d End
Do try=1 To tries
Call time 'R'
zz=0
Do d=1 To dots
Parse Var training.d inputs.0 inputs.1 inputs.2 answer.d
Call train d
Do ii=1 To d
Parse Var training.ii inputs.0 inputs.1 inputs.2 answer.d
guess = feedForward(d)
End
End
Call show try
End
Exit
show:
Parse Arg run
show=wordpos(run,'0 1' tries)>0
If run>0 Then Say ' '
If show Then Say 'Point x f(x) r y ff ok zz'
zz=0
Do d=1 To dots
x=x.d
y=y.d
Parse Value x.d y.d 1 with inputs.0 inputs.1 inputs.2
ff=format(feedForward(),2)
Select
When f(x)<y Then r='<'
When f(x)>y Then r='>'
Otherwise r='='
End
If r='<' & ff=1 |,
r='>' & ff=-1 Then Do; tag='ok'; zz=zz+1; End
Else tag='--'
If show Then
Say format(d,5) format(x,4,0) format(f(x),4,0) r format(y,4,0) right(ff,2),
tag format(zz,4)
End
If show Then Say copies('-',33)
weights=format(weights.0,2,5) format(weights.1,2,5) format(weights.2,2,5)
Select
When run=0 Then txt='Initial pattern'
When run=1 Then txt='After one loop '
Otherwise txt='After' run 'loops'
End
Say left(txt,15) format(zz,4) 'points fire. weights='weights
Return
train: Procedure Expose inputs. weights.
desired=sign(inputs.1-f(inputs.0)) guess = feedForward() error = desired-guess Do i=0 To 2 weights.i=weights.i+0.00001*error*inputs.i End Return
f: Return arg(1)*0.7+40
nextDouble: /* random number between -1 and +1 */
Return random(100000)/100000
feedforward: Procedure Expose inputs. weights.
sum=0 Do i=0 To 2 sum=sum+inputs.i*weights.i End Return activate(sum)
activate:
If arg(1)>0 Then Return 1
Else Return -1
init:
Call random 10000,10000,333 /* seed the random function */ dots=30 width=640 height=360 tries=10 Do i=0 To 2 weights.i=nextDouble() End Do i=1 To dots x.i=nextDouble()*width y.i=nextDouble()*height End Return</lang>
- Output:
Point x f(x) r y ff ok zz
1 100 110 < 204 1 ok 1
2 613 469 > 117 1 -- 1
3 528 409 > 125 1 -- 1
4 141 139 > 119 1 -- 1
5 32 62 < 245 1 ok 2
6 11 48 < 336 1 ok 3
7 435 344 > 270 1 -- 3
8 572 440 > 280 1 -- 3
9 442 350 > 141 1 -- 3
10 410 327 > 209 1 -- 3
11 290 243 < 355 1 ok 4
12 257 220 < 260 1 ok 5
13 235 205 > 51 1 -- 5
14 600 460 > 66 1 -- 5
15 21 55 < 182 1 ok 6
16 197 178 > 42 1 -- 6
17 444 351 > 150 1 -- 6
18 393 315 > 87 1 -- 6
19 622 475 > 280 1 -- 6
20 436 345 > 292 1 -- 6
21 553 427 > 261 1 -- 6
22 478 374 > 264 1 -- 6
23 373 301 > 120 1 -- 6
24 527 409 > 94 1 -- 6
25 558 431 > 49 1 -- 6
26 616 471 > 358 1 -- 6
27 241 209 > 68 1 -- 6
28 365 295 > 164 1 -- 6
29 371 299 > 155 1 -- 6
30 102 112 < 220 1 ok 7
---------------------------------
Initial pattern 7 points fire. weights= 0.28732 0.50931 0.45298
Point x f(x) r y ff ok zz
1 100 110 < 204 1 ok 1
2 613 469 > 117 1 -- 1
3 528 409 > 125 1 -- 1
4 141 139 > 119 1 -- 1
5 32 62 < 245 1 ok 2
6 11 48 < 336 1 ok 3
7 435 344 > 270 1 -- 3
8 572 440 > 280 1 -- 3
9 442 350 > 141 1 -- 3
10 410 327 > 209 1 -- 3
11 290 243 < 355 1 ok 4
12 257 220 < 260 1 ok 5
13 235 205 > 51 1 -- 5
14 600 460 > 66 1 -- 5
15 21 55 < 182 1 ok 6
16 197 178 > 42 1 -- 6
17 444 351 > 150 1 -- 6
18 393 315 > 87 1 -- 6
19 622 475 > 280 1 -- 6
20 436 345 > 292 1 -- 6
21 553 427 > 261 1 -- 6
22 478 374 > 264 1 -- 6
23 373 301 > 120 1 -- 6
24 527 409 > 94 1 -- 6
25 558 431 > 49 1 -- 6
26 616 471 > 358 1 -- 6
27 241 209 > 68 1 -- 6
28 365 295 > 164 1 -- 6
29 371 299 > 155 1 -- 6
30 102 112 < 220 1 ok 7
---------------------------------
After one loop 7 points fire. weights= 0.08433 0.43412 0.45252
After 2 loops 16 points fire. weights=-0.10749 0.35991 0.45208
After 3 loops 26 points fire. weights=-0.18168 0.31845 0.45192
After 4 loops 28 points fire. weights=-0.20192 0.30482 0.45186
After 5 loops 29 points fire. weights=-0.20473 0.30245 0.45184
After 6 loops 29 points fire. weights=-0.20755 0.30007 0.45182
After 7 loops 29 points fire. weights=-0.21037 0.29769 0.45180
After 8 loops 29 points fire. weights=-0.21319 0.29532 0.45178
After 9 loops 29 points fire. weights=-0.21601 0.29294 0.45176
Point x f(x) r y ff ok zz
1 100 110 < 204 1 ok 1
2 613 469 > 117 -1 ok 2
3 528 409 > 125 -1 ok 3
4 141 139 > 119 1 -- 3
5 32 62 < 245 1 ok 4
6 11 48 < 336 1 ok 5
7 435 344 > 270 -1 ok 6
8 572 440 > 280 -1 ok 7
9 442 350 > 141 -1 ok 8
10 410 327 > 209 -1 ok 9
11 290 243 < 355 1 ok 10
12 257 220 < 260 1 ok 11
13 235 205 > 51 -1 ok 12
14 600 460 > 66 -1 ok 13
15 21 55 < 182 1 ok 14
16 197 178 > 42 -1 ok 15
17 444 351 > 150 -1 ok 16
18 393 315 > 87 -1 ok 17
19 622 475 > 280 -1 ok 18
20 436 345 > 292 -1 ok 19
21 553 427 > 261 -1 ok 20
22 478 374 > 264 -1 ok 21
23 373 301 > 120 -1 ok 22
24 527 409 > 94 -1 ok 23
25 558 431 > 49 -1 ok 24
26 616 471 > 358 -1 ok 25
27 241 209 > 68 -1 ok 26
28 365 295 > 164 -1 ok 27
29 371 299 > 155 -1 ok 28
30 102 112 < 220 1 ok 29
---------------------------------
After 10 loops 29 points fire. weights=-0.21883 0.29057 0.45174
Scala
Java Swing Interoperability
<lang Scala>import java.awt._ import java.awt.event.ActionEvent
import javax.swing._
import scala.util.Random
object Perceptron extends App {
SwingUtilities.invokeLater(() =>
new JFrame("Perceptron") {
class Perceptron(val n: Int) extends JPanel {
private val (c, dim) = (0.00001, new Dimension(640, 360))
private val (random, training) = (new Random, Array.ofDim[Trainer](2000))
private val weights = Array.fill(n)(random.nextDouble * 2 - 1)
private var count = 0
override def paintComponent(gg: Graphics): Unit = {
var x = getWidth
var y = f(x).toInt
def train(inputs: Array[Double], desired: Int): Unit = {
val guess = feedForward(inputs)
for (i <- weights.indices) weights(i) += c * (desired - guess) * inputs(i)
}
def feedForward(inputs: Array[Double]) = {
assert(inputs.length == weights.length, "weights and input length mismatch")
var sum = 0.0
for (i <- weights.indices) {
sum += inputs(i) * weights(i)
}
if (sum > 0) 1 else -1
}
super.paintComponent(gg)
val g = gg.asInstanceOf[Graphics2D]
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
// we're drawing upside down
g.setStroke(new BasicStroke(2))
g.setColor(Color.orange)
g.drawLine(0, f(0).toInt, x, y)
train(training(count).inputs, training(count).answer)
count = (count + 1) % training.length
g.setStroke(new BasicStroke(1))
g.setColor(Color.black)
for (i <- 0 until count) {
val guess = feedForward(training(i).inputs)
x = training(i).inputs(0).toInt - 4
y = training(i).inputs(1).toInt - 4
if (guess > 0) g.drawOval(x, y, 8, 8)
else g.fillOval(x, y, 8, 8)
}
}
private def f(x: Double) = x * 0.7 + 40
class Trainer(val x: Double, val y: Double, var answer: Int) {
val inputs = Array[Double](x, y, 1)
}
for (j <- training.indices;
x = random.nextDouble * dim.width;
y = random.nextDouble * dim.height;
answer = if (y < f(x)) -1 else 1
) training(j) = new Trainer(x, y, answer)
new Timer(10, (e: ActionEvent) => repaint()).start()
setBackground(Color.white)
setPreferredSize(dim)
}
add(new Perceptron(3), BorderLayout.CENTER)
pack()
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
setLocationRelativeTo(null)
setResizable(false)
setVisible(true)
})
}</lang>
Scheme
<lang scheme>(import (scheme base)
(scheme case-lambda)
(scheme write)
(srfi 27)) ; for random numbers
(random-source-randomize! default-random-source)
- Function to create a perceptron
- num-inputs
- size of input data
- learning-rate
- small number, to give rate of learning
- returns perceptron as a function
- accepting 'train data -> trains on given list of data
- 'test data -> returns percent correct on given list of data
- 'show -> displays the perceptron weights
- classes assumed to be 1, -1
(define (create-perceptron num-inputs learning-rate)
(define (make-rnd-vector n) ; rnd vector, values in [-1,1]
(let ((result (make-vector n)))
(do ((i 0 (+ 1 i)))
((= i n) result)
(vector-set! result i (- (* 2 (random-real)) 1)))))
(define (extended input) ; add a 1 to end of vector
(let* ((n (vector-length input))
(result (make-vector (+ 1 n))))
(do ((i 0 (+ 1 i)))
((= i n) (vector-set! result i 1)
result)
(vector-set! result i (vector-ref input i)))))
(define (predict weights extended-input)
(let ((sum 0))
(vector-for-each (lambda (w i) (set! sum (+ sum (* w i))))
weights extended-input)
(if (positive? sum) 1 -1)))
;
(let ((weights (make-rnd-vector (+ 1 num-inputs))))
(case-lambda ; defines a function for the perceptron
((key)
(when (eq? key 'show)
(display weights) (newline)))
((action data)
(case action
((train)
(for-each
(lambda (datum)
(let* ((extended-input (extended (car datum)))
(error (- (cdr datum) (predict weights extended-input))))
(set! weights (vector-map (lambda (w i) (+ w (* learning-rate error i)))
weights
extended-input))))
data))
((test)
(let ((count 0))
(for-each
(lambda (datum) (when (= (cdr datum) (predict weights (extended (car datum))))
(set! count (+ 1 count))))
data)
(inexact (* 100 (/ count (length data)))))))))))
- create data
- list of n ( #(input values) . target ) pairs
- using formula y = mx + b, target based on if input above / below line
(define (create-data m b n)
(define (target x y)
(let ((fx (+ b (* m x))))
(if (< fx y) 1 -1)))
(define (create-datum)
(let ((x (random-real))
(y (random-real)))
(cons (vector x y) (target x y))))
;
(do ((data '() (cons (create-datum) data)))
((= n (length data)) data)))
- train on 5000 points, show weights and result on 1000 test points
(let* ((m 0.7)
(b 0.2)
(perceptron (create-perceptron 2 0.001)))
(perceptron 'train (create-data m b 5000))
(perceptron 'show)
(display "Percent correct on test set: ")
(display (perceptron 'test (create-data m b 1000)))
(newline))
- show performance along training stages
(let* ((m 0.7) ; gradient of target line
(b 0.2) ; y-intercept of target line
(train-step 1000) ; step in training set size
(train-stop 20000) ; largest training set size
(test-set (create-data m b 1000)) ; create a fixed test set
(perceptron (create-perceptron 2 0.001)))
(do ((i train-step (+ i train-step)))
((> i train-stop) )
(perceptron 'train (create-data m b train-step))
(display (string-append "Trained on " (number->string i)
", percent correct is "
(number->string (perceptron 'test test-set))
"\n"))))</lang>
- Output:
#(-0.5914540100624854 1.073343782042039 -0.29780862758499393) Percent correct on test set: 95.4 Trained on 1000, percent correct is 18.1 Trained on 2000, percent correct is 91.1 Trained on 3000, percent correct is 98.0 Trained on 4000, percent correct is 92.5 Trained on 5000, percent correct is 98.6 Trained on 6000, percent correct is 98.6 Trained on 7000, percent correct is 98.8 Trained on 8000, percent correct is 97.8 Trained on 9000, percent correct is 99.1 Trained on 10000, percent correct is 96.0 Trained on 11000, percent correct is 98.6 Trained on 12000, percent correct is 98.2 Trained on 13000, percent correct is 99.2 Trained on 14000, percent correct is 99.4 Trained on 15000, percent correct is 99.0 Trained on 16000, percent correct is 98.8 Trained on 17000, percent correct is 97.5 Trained on 18000, percent correct is 99.8 Trained on 19000, percent correct is 99.2 Trained on 20000, percent correct is 100.0
XLISP
Like the Pascal example, this is a text-based program using a 20x20 grid. It is slightly more general, however, because it allows the function that is to be learnt and the perceptron's bias and learning constant to be passed as arguments to the trainer and perceptron objects. <lang scheme>(define-class perceptron
(instance-variables weights bias learning-constant) )
(define-method (perceptron 'initialize b lc)
(defun random-weights (n)
(if (> n 0)
(cons (- (/ (random 20000) 10000) 1) (random-weights (- n 1))) ) )
(setq weights (random-weights 3))
(setq bias b)
(setq learning-constant lc)
self )
(define-method (perceptron 'value x y)
(if (> (+ (* x (car weights)) (* y (cadr weights)) (* bias (caddr weights))) 0) 1 -1 ) )
(define-method (perceptron 'print-grid)
(print-row self 10) )
(define-method (perceptron 'learn source runs)
(defun learn-row (row)
(defun learn-cell (cell)
(define inputs `(,cell ,row ,bias))
(define error (- (source 'value cell row) (self 'value cell row)))
(defun reweight (ins ws)
(if (car ins)
(cons (+ (car ws) (* error (car ins) learning-constant)) (reweight (cdr ins) (cdr ws))) ) )
(setq weights (reweight inputs weights))
(if (< cell 10)
(learn-cell (+ cell 1)) ) )
(learn-cell -9)
(if (> row -9)
(learn-row (- row 1)) ) )
(do ((i 1 (+ i 1))) ((> i runs))
(learn-row 10) ) )
(define-class trainer
(instance-variables fn) )
(define-method (trainer 'initialize function)
(setq fn function) self )
(define-method (trainer 'print-grid)
(print-row self 10) )
(define-method (trainer 'value x y)
(if (apply fn `(,x ,y))
1
-1 ) )
(defun print-row (obj row)
(defun print-cell (cell)
(if (= (obj 'value cell row) 1)
(display "#")
(display "O") )
(if (< cell 10)
(print-cell (+ cell 1))
(newline) ) )
(print-cell -9)
(if (> row -9)
(print-row obj (- row 1))
(newline) ) )
(define ptron (perceptron 'new 1 0.01))
(define training (trainer 'new
(lambda (x y) (> y (+ (* x 2) 1))) ) )
(newline) (display "Target output for y = 2x + 1:") (newline) (training 'print-grid) (display "Output from untrained perceptron:") (newline) (ptron 'print-grid) (display "Output from perceptron after 1 training run:") (newline) (ptron 'learn training 1) (ptron 'print-grid) (display "Output from perceptron after 5 training runs:") (newline) (ptron 'learn training 4) (ptron 'print-grid)</lang>
- Output:
Target output for y = 2x + 1: ##############OOOOOO #############OOOOOOO #############OOOOOOO ############OOOOOOOO ############OOOOOOOO ###########OOOOOOOOO ###########OOOOOOOOO ##########OOOOOOOOOO ##########OOOOOOOOOO #########OOOOOOOOOOO #########OOOOOOOOOOO ########OOOOOOOOOOOO ########OOOOOOOOOOOO #######OOOOOOOOOOOOO #######OOOOOOOOOOOOO ######OOOOOOOOOOOOOO ######OOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO ####OOOOOOOOOOOOOOOO Output from untrained perceptron: ######OOOOOOOOOOOOOO ######OOOOOOOOOOOOOO #######OOOOOOOOOOOOO #######OOOOOOOOOOOOO #######OOOOOOOOOOOOO ########OOOOOOOOOOOO ########OOOOOOOOOOOO ########OOOOOOOOOOOO #########OOOOOOOOOOO #########OOOOOOOOOOO #########OOOOOOOOOOO ##########OOOOOOOOOO ##########OOOOOOOOOO ##########OOOOOOOOOO ###########OOOOOOOOO ###########OOOOOOOOO ###########OOOOOOOOO ############OOOOOOOO ############OOOOOOOO ############OOOOOOOO Output from perceptron after 1 training run: ###############OOOOO ###############OOOOO ##############OOOOOO ##############OOOOOO #############OOOOOOO ############OOOOOOOO ############OOOOOOOO ###########OOOOOOOOO ##########OOOOOOOOOO ##########OOOOOOOOOO #########OOOOOOOOOOO #########OOOOOOOOOOO ########OOOOOOOOOOOO #######OOOOOOOOOOOOO #######OOOOOOOOOOOOO ######OOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO ####OOOOOOOOOOOOOOOO ####OOOOOOOOOOOOOOOO Output from perceptron after 5 training runs: ##############OOOOOO #############OOOOOOO #############OOOOOOO ############OOOOOOOO ############OOOOOOOO ###########OOOOOOOOO ###########OOOOOOOOO ##########OOOOOOOOOO ##########OOOOOOOOOO #########OOOOOOOOOOO #########OOOOOOOOOOO ########OOOOOOOOOOOO ########OOOOOOOOOOOO #######OOOOOOOOOOOOO #######OOOOOOOOOOOOO ######OOOOOOOOOOOOOO ######OOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO #####OOOOOOOOOOOOOOO ####OOOOOOOOOOOOOOOO
zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>class Perceptron{
const c=0.00001;
var [const] W=640, H=350;
fcn init(n){
r:=(0.0).random.fp(1); // r()-->[0..1)
var weights=n.pump(List(),'wrap(){ r()*2 - 1 }), // Float[n]
training=(2000).pump(List,'wrap(){ // (x,y,1,answer)[2000]
x,y,answer:=r()*W, r()*H, (if(y<f(x)) -1 or 1);
return(x,y,1,answer) });
}
fcn f(x){ 0.7*x + 40 } // a line
fcn feedForward(xy1a){
sum:=0.0;
foreach i in (weights.len()){ sum+=xy1a[i]*weights[i] }
(sum<0) and -1 or 1 // activate(sum)
}
fcn train(xy1a){
guess,error:=feedForward(xy1a), xy1a[-1] - guess;
foreach i in (weights.len()){ weights[i]+=c*error*xy1a[i] }
}
}</lang> <lang zkl>p:=Perceptron(3); p.training.apply2(p.train);
PPM:=Import("ppm.zkl").PPM; pixmap:=PPM(p.W+20,p.H+20,0xFF|FF|FF);
foreach xy1a in (p.training){
guess,x,y:=p.feedForward(xy1a), 8 + xy1a[0], 8 + xy1a[1]; color:=(if(guess>0) 0 else 0xFF|00|00); // black or red pixmap.circle(x,y,8,color);
} pixmap.writeJPGFile("perceptron.zkl.jpg");</lang>
- Output:
