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{{draft task}} A [[wp:Perceptron|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 [http://natureofcode.com/book/chapter-10-neural-networks/ 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
- [http://natureofcode.com/book/chapter-10-neural-networks/ Neural networks (nature of code)]
- [https://youtu.be/dXuNAkHsos4?t=16m44s Machine Learning - Perceptrons (youtube)]
Forth
{{works with|GNU Forth}}
Where it says [email protected] it should say f@.
require random.fs
here seed !
warnings off
( THE PERCEPTRON )
: randomWeight 2000 random 1000 - s>f 1000e f/ ;
: createPerceptron create dup , 0 ?DO randomWeight f, LOOP ;
variable arity
variable ^weights
variable ^inputs
: perceptron! dup @ arity ! cell+ ^weights ! ;
: inputs! ^inputs ! ;
0.0001e fconstant learningConstant
: activate 0e f> IF 1e ELSE -1e THEN ;
: feedForward
^weights @ ^inputs @ 0e
arity @ 0 ?DO
dup f@ float + swap
dup f@ float + swap
f* f+
LOOP 2drop activate ;
: train
feedForward f- learningConstant f*
^weights @ ^inputs @
arity @ 0 ?DO
fdup dup f@ f* float + swap
dup f@ f+ dup f! float + swap
LOOP 2drop fdrop ;
( THE TRAINER )
create point 0e f, 0e f, 1e f, \ x y bias
: x point ;
: y point float + ;
: randomX 640 random s>f ;
: randomY 360 random s>f ;
\ y = Ax + B
2e fconstant A
1e fconstant B
: randomizePoint
randomY fdup y f!
randomX fdup x f!
A f* B f+ f< IF -1e ELSE 1e THEN ;
3 createPerceptron myPerceptron
variable trainings
10000 constant #rounds
: setup 0 ; \ success counter
: calculate s>f #rounds s>f f/ 100e f* ;
: report ." After " trainings @ . ." trainings: "
calculate f. ." % accurate" cr ;
: check learningConstant f~ IF 1+ THEN ;
: evaluate randomizePoint feedForward check ;
: evaluate setup #rounds 0 ?DO evaluate LOOP report ;
: tally 1 trainings +! ;
: timesTrain 0 ?DO randomizePoint train tally LOOP ;
: initialize
myPerceptron perceptron!
point inputs!
0 trainings ! ;
: go
initialize evaluate
1 timesTrain evaluate
1 timesTrain evaluate
1 timesTrain evaluate
1 timesTrain evaluate
1 timesTrain evaluate
5 timesTrain evaluate
10 timesTrain evaluate
30 timesTrain evaluate
50 timesTrain evaluate
100 timesTrain evaluate
300 timesTrain evaluate
500 timesTrain evaluate ;
go bye
Example output:
After 0 trainings: 10.16 % accurate
After 1 trainings: 7.43 % accurate
After 2 trainings: 7.71 % accurate
After 3 trainings: 4.93 % accurate
After 4 trainings: 3.11 % accurate
After 5 trainings: 0.6 % accurate
After 10 trainings: 48.72 % accurate
After 20 trainings: 85.55 % accurate
After 50 trainings: 86.36 % accurate
After 100 trainings: 98.59 % accurate
After 200 trainings: 98.84 % accurate
After 500 trainings: 95.86 % accurate
After 1000 trainings: 99.8 % accurate
Go
{{libheader|Go Graphics}}
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.
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")
}
Java
{{works with|Java|8}}
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);
});
}
}
JavaScript
Uses P5 lib.
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];
}
}
}
[[File:perceptronJS.png]]
Well, it seems I cannot upload an image :(
Julia
# file module.jl
module SimplePerceptrons
# default activation function
step(x) = x > 0 ? 1 : -1
mutable struct Perceptron{T, F}
weights::Vector{T}
lr::T
activate::F
end
Perceptron{T}(n::Integer, lr = 0.01, f::Function = step) where T =
Perceptron{T, typeof(f)}(2 .* rand(n + 1) .- 1, lr, f)
Perceptron(args...) = Perceptron{Float64}(args...)
@views predict(p::Perceptron, x::AbstractVector) = p.activate(p.weights[1] + x' * p.weights[2:end])
@views predict(p::Perceptron, X::AbstractMatrix) = p.activate.(p.weights[1] .+ X * p.weights[2:end])
function train!(p::Perceptron, X::AbstractMatrix, y::AbstractVector; epochs::Integer = 100)
for _ in Base.OneTo(epochs)
yhat = predict(p, X)
err = y .- yhat
ΔX = p.lr .* err .* X
for ind in axes(ΔX, 1)
p.weights[1] += err[ind]
p.weights[2:end] .+= ΔX[ind, :]
end
end
return p
end
accuracy(p, X::AbstractMatrix, y::AbstractVector) = count(y .== predict(p, X)) / length(y)
end # module SimplePerceptrons
# file _.jl
const SP = include("module.jl")
p = SP.Perceptron(2, 0.1)
a, b = 0.5, 1
X = rand(1000, 2)
y = map(x -> x[2] > a + b * x[1] ? 1 : -1, eachrow(X))
# Accuracy
@show SP.accuracy(p, X, y)
# Train
SP.train!(p, X, y, epochs = 1000)
ahat, bhat = p.weights[1] / p.weights[2], -p.weights[3] / p.weights[2]
using Plots
scatter(X[:, 1], X[:, 2], markercolor = map(x -> x == 1 ? :red : :blue, y))
Plots.abline!(b, a, label = "real line", linecolor = :red, linewidth = 2)
SP.train!(p, X, y, epochs = 1000)
ahat, bhat = p.weights[1] / p.weights[2], -p.weights[3] / p.weights[2]
Plots.abline!(bhat, ahat, label = "predicted line")
Kotlin
{{trans|Java}}
// 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
}
}
}
Lua
Simple implementation allowing for any number of inputs (in this case, just 1), testing of the Perceptron, and training.
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
{{out}}
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.
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.
{{out}}
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
Phix
{{libheader|pGUI}} Interactive GUI version. Select one of five lines, set the number of points, learning constant, learning rate, and max iterations. Plots accuracy vs. iterations and displays the training data in blue/black=above/incorrect and green/red=below/incorrect [all blue/green = 100% accurate].
-- demo\rosetta\Perceptron.exw
--
-- The learning curve turned out more haphazard than I imagined, and adding a
-- non-linear line to f() (case 5) was perhaps not such a great idea given how
-- much it sometimes struggles with some of the other straight lines anyway.
--
include pGUI.e
--#withtype Ihandle
--#withtype Ihandles
--#withtype cdCanvas
constant help_txt = """
A perceptron is the simplest possible neural network, consisting of just one neuron
that we train to recognise whether a point is above or below a given straight line.
NB: It would probably be unwise to overly assume that this could easily be adapted
to anything more complex, or actually useful. It is just a basic introduction, but
you have to start somewhere. What is interesting is that ultimately the neuron is
just three numbers, plus a bucket-load of training gumpf.
The left hand panel allows settings to be changed, in the middle we plot the rate of
learning, and on the right we show the training data colour coded as above/below and
correct/incorrect (blue/black=above/incorrect, green/red=below/incorrect). What you
want to see is all blue/green, with no black/red.
You can change the line algorithm (four straight and one curved that it is not meant
to be able to cope with), the number of points (size of training data), the learning
constant, learning rate (iterations/second) and the maximum number of iterations.
Note that training automatically stops once 100% accuracy is reached (since the error
is then always zero, no further changes would ever occur). Also note that a restart
is triggered when any setting is changed, not just when the restart button is pressed.
The learning curve was expected to start at 50% (random chance of being right) and
gradually improve towards 100%, except when the non-linear line was selected. It
turned out far more haphazard than I thought it would. Originally it allowed up to
10,000,000 iterations, but it rarely improved much beyond 1,000,000."""
function help_cb(Ihandln /*help*/)
IupMessage("Perceptron",help_txt)
return IUP_DEFAULT
end function
Ihandle dlg, plot, canvas, timer,
iteration, accuracy, w1, w2, w3
cdCanvas cddbuffer, cdcanvas
integer line_alg = 1
integer points = 2000,
learning_rate = 10000,
max_iterations = 1_000_000,
total_iterations = 0
atom learning_constant = 0.00001
enum WEIGHTS, -- The actual neuron (just 3 numbers)
TRAINING -- training data/results, variable length
enum INPUTS, ANSWER -- contents of [TRAINING]
-- note that length(inputs[i]) must = length(weights)
sequence perceptron = {},
last_wh -- (recreate "" on resize)
function activate(atom t)
return iff(t>0?+1:-1)
end function
function f(atom x)
switch line_alg
case 1: return x*0.7+40
case 2: return 300-0.3*x
case 3: return x*0.75
case 4: return 2*x+1
case 5: return x/2+sin(x/100)*100+100 -- (fail)
end switch
end function
procedure new_perceptron(integer n)
sequence weights := repeat(0, n)
for i=1 to n do
weights[i] = rnd()*2 - 1
end for
sequence training := repeat(0,points)
integer {w,h} = last_wh
for i=1 to points do
integer x := rand(w),
y := rand(h),
answer := activate(y-f(x))
sequence inputs = {x, y, 1}
-- aside: inputs is {x,y,1}, rather than {x,y} because an
-- input of {0,0} could only ever yield 0, whereas
-- {0,0,1} can yield a non-zero guess: weights[3].
training[i] = {inputs, answer} -- {INPUTS, ANSWER}
end for
perceptron = {weights, training} -- {WEIGHTS, TRAINING}
end procedure
function feed_forward(sequence inputs)
if length(inputs)!=length(perceptron[WEIGHTS]) then
throw("weights and input length mismatch, program terminated")
end if
atom total := 0.0
for i=1 to length(inputs) do
total += inputs[i] * perceptron[WEIGHTS][i]
end for
return activate(total)
end function
procedure train(sequence inputs, integer desired)
integer guess := feed_forward(inputs),
error := desired - guess
for i=1 to length(perceptron[WEIGHTS]) do
perceptron[WEIGHTS][i] += learning_constant * error * inputs[i]
end for
end procedure
--DEV add to pGUI/doc
procedure cdCanvasCircle(cdCanvas cddbuffer, atom x, y, r)
cdCanvasArc(cddbuffer,x,y,r,r,0,360)
end procedure
function draw(bool bDraw=true)
-- (if bDraw is false, we just want the "correct" count)
integer correct = 0
atom x, y
for i=1 to points do
{sequence inputs, integer answer} = perceptron[TRAINING][i]
integer guess := feed_forward(inputs)
correct += (guess=answer)
if bDraw then
{x,y} = inputs
-- blue/black=above/incorrect, green/red=below/incorrect
integer clr = iff(guess=answer?iff(guess>0?CD_BLUE:CD_GREEN)
:iff(guess>0?CD_BLACK:CD_RED))
cdCanvasSetForeground(cddbuffer, clr)
cdCanvasCircle(cddbuffer, x, y, 8)
end if
end for
if bDraw then
cdCanvasSetForeground(cddbuffer, CD_BLACK)
x := last_wh[1]
y := f(x)
if line_alg=5 then
-- non-linear so (crudely) draw in little segments
for i=0 to x by 20 do
cdCanvasLine(cddbuffer,i,f(i),i+20,f(i+20))
end for
else
cdCanvasLine(cddbuffer,0,f(0),x,y)
end if
end if
return correct
end function
bool re_plot = true
atom plot0
sequence plotx = repeat(0,19),
ploty = repeat(0,19)
integer imod = 1, -- keep every 1, then 10, then 100, ...
pidx = 1
function restart_cb(Ihandln /*restart*/)
last_wh = IupGetIntInt(canvas, "DRAWSIZE")
new_perceptron(3)
imod = 1
pidx = 1
total_iterations = 0
plot0 = (draw(false)/points)*100
re_plot = true
IupSetInt(timer,"RUN",1)
return IUP_DEFAULT
end function
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
if perceptron={}
or last_wh!=IupGetIntInt(canvas, "DRAWSIZE") then
{} = restart_cb(NULL)
end if
cdCanvasActivate(cddbuffer)
cdCanvasClear(cddbuffer)
integer correct = draw()
cdCanvasFlush(cddbuffer)
if re_plot then
re_plot = false
IupSetAttribute(plot, "CLEAR", NULL)
IupPlotBegin(plot)
IupPlotAdd(plot, 0, plot0)
for i=1 to pidx-1 do
IupPlotAdd(plot, plotx[i], ploty[i])
end for
{} = IupPlotEnd(plot)
IupSetAttribute(plot, "REDRAW", NULL)
end if
IupSetStrAttribute(iteration,"TITLE","iteration: %d",{total_iterations})
IupSetStrAttribute(w1,"TITLE","%+f",{perceptron[WEIGHTS][1]})
IupSetStrAttribute(w2,"TITLE","%+f",{perceptron[WEIGHTS][2]})
IupSetStrAttribute(w3,"TITLE","%+f",{perceptron[WEIGHTS][3]})
IupSetStrAttribute(accuracy,"TITLE","accuracy: %.4g%%",{(correct/points)*100})
IupRefresh({iteration,w1,w2,w3,accuracy}) -- (force label resize)
if correct=points then
IupSetInt(timer,"RUN",0) -- stop at 100%
end if
return IUP_DEFAULT
end function
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_PARCHMENT)
return IUP_DEFAULT
end function
function valuechanged_cb(Ihandle ih)
string name = IupGetAttribute(ih, "NAME")
integer v = IupGetInt(ih, "VALUE")
switch name
case "line": line_alg = v
case "points": points = power(10,v)
case "learn": learning_constant = power(10,-v)
case "rate": learning_rate = power(10,v-1)
case "max": max_iterations = power(10,v)
end switch
{} = restart_cb(NULL)
return IUP_DEFAULT
end function
function timer_cb(Ihandle /*timer*/)
for i=1 to min(learning_rate,max_iterations) do
total_iterations += 1
integer c = mod(total_iterations,points)+1
train(perceptron[TRAINING][c][INPUTS], perceptron[TRAINING][c][ANSWER])
if mod(total_iterations,imod)=0 then
-- save 1,2..10, then 20,30,..100, then 200,300,..1000, etc
re_plot = true
plotx[pidx] = total_iterations
ploty[pidx] = (draw(false)/points)*100
if pidx=10 or pidx=19 then
if pidx=19 then
-- drop (eg) 1,2,..9, replace with 10,20,..90,
-- next time replace 10,20..90 with 100,200..900, etc
plotx[1..10] = plotx[10..19]
ploty[1..10] = ploty[10..19]
end if
imod *= 10
pidx = 11
else
pidx += 1
end if
end if
end for
if total_iterations>=max_iterations then
IupSetInt(timer,"RUN",0)
end if
IupUpdate(canvas)
return IUP_IGNORE
end function
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
if c=K_F1 then return help_cb(NULL) end if
if c=K_F5 then return restart_cb(NULL) end if
return IUP_CONTINUE
end function
function settings(string lname, name, sequence opts, integer v=1)
Ihandle lbl = IupLabel(lname,"PADDING=0x4"),
list = IupList("NAME=%s, DROPDOWN=YES",{name}),
hbox = IupHbox({lbl,IupFill(),list})
for i=1 to length(opts) do
IupSetAttributeId(list,"",i,opts[i])
end for
IupSetInt(list,"VISIBLEITEMS",length(opts)+1)
IupSetInt(list,"VALUE",v)
IupSetCallback(list, "VALUECHANGED_CB", Icallback("valuechanged_cb"));
return hbox
end function
function sep()
return IupLabel("","SEPARATOR=HORIZONTAL")
end function
procedure main()
IupOpen()
IupControlsOpen()
Ihandle settings_lbl = IupHbox({IupFill(),IupLabel("Settings"),IupFill()}),
line = settings("line","line",{"x*0.7 + 40","300 - 0.3*x","x*0.75","2*x + 1","x/2+sin(x/100)*100+100"}),
points = settings("number of points","points",{"10","100","1000","10000"},3),
learn = settings("learning constant","learn",{"0.1","0.01","0.001","0.0001","0.00001"},5),
rate = settings("learning rate","rate",{"1/s","10/s","100/s","1000/s","10000/s"},5),
maxiter = settings("max iterations","max",{"10","100","1000","10,000","100,000","1,000,000"},6),
restart = IupButton("Restart (F5)", "ACTION", Icallback("restart_cb")),
helpbtn = IupButton("Help (F1)", "ACTION", Icallback("help_cb")),
buttons = IupHbox({restart,IupFill(),helpbtn})
iteration = IupLabel("iteration: 1")
w1 = IupLabel("1")
w2 = IupLabel("2")
w3 = IupLabel("3")
Ihandle weights = IupHbox({IupLabel("weights: ","PADDING=0x4"),IupVbox({w1,w2,w3})})
accuracy = IupLabel("accuracy: 12.34%")
Ihandle vbox = IupVbox({settings_lbl, sep(),
line, sep(), points, sep(), learn, sep(),
rate, sep(), maxiter, sep(), buttons, sep(),
IupHbox({iteration}), weights, IupHbox({accuracy})})
IupSetAttribute(vbox, "GAP", "4");
plot = IupPlot("MENUITEMPROPERTIES=Yes")
IupSetAttribute(plot, "TITLE", "Learning Curve");
IupSetAttribute(plot, "TITLEFONTSIZE", "10");
IupSetAttribute(plot, "TITLEFONTSTYLE", "ITALIC");
IupSetAttribute(plot, "GRIDLINESTYLE", "DOTTED");
IupSetAttribute(plot, "GRID", "YES");
IupSetAttribute(plot, "AXS_XLABEL", "iterations");
IupSetAttribute(plot, "AXS_YLABEL", "% correct");
IupSetAttribute(plot, "AXS_XFONTSTYLE", "ITALIC");
IupSetAttribute(plot, "AXS_YFONTSTYLE", "ITALIC");
IupSetAttribute(plot, "AXS_XTICKNUMBER", "No");
IupSetAttribute(plot, "AXS_YAUTOMIN", "No");
IupSetAttribute(plot, "AXS_YAUTOMAX", "No");
IupSetInt(plot, "AXS_YMIN", 0)
IupSetInt(plot, "AXS_YMAX", 100)
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "640x360") -- initial size
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
Ihandle hbox = IupHbox({vbox, plot, canvas},"MARGIN=4x4, GAP=10")
dlg = IupDialog(hbox);
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupSetAttribute(dlg, "TITLE", "Perceptron")
IupMap(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release limitation
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
timer = IupTimer(Icallback("timer_cb"), 100) -- (was 1 sec, now 0.1s)
IupMainLoop()
IupClose()
end procedure
main()
Racket
{{trans|Java}}
#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))
Run it and see the image for yourself, I can't get it onto RC!
REXX
{{trans|Java}}
/* 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
{{out}}
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
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)
})
}
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"))))
{{out}}
#(-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
Smalltalk
{{works with|GNU Smalltalk}}
Number extend [
activate
[^self > 0 ifTrue: [1] ifFalse: [-1]]
]
Object subclass: Perceptron [
| weights |
feedForward: inputArray
[^(self sumOfWeighted: inputArray) activate]
train: inputArray desire: expected
[| actual error |
actual := self feedForward: inputArray.
error := 0.0001 * (expected - actual).
weights := weights
with: inputArray
collect: [:weight :input | weight + (error * input)]]
sumOfWeighted: inputArray
[^(self weighted: inputArray)
inject: 0
into: [:each :sum | each + sum]]
weighted: inputArray
[^weights
with: inputArray
collect: [:weight :input | weight * input]]
Perceptron class >> new: arity
[^self basicNew
initialize: arity;
yourself]
initialize: arity
[weights := 1
to: arity
collect: [:x | self randomWeight]]
randomWeight
[^(Random between: -1000 and: 1000) / 1000]
]
Perceptron class extend [
| perceptron trainings input expected actual |
evaluationSamples := 100000.
initializeTest
[perceptron := self new: 3.
input := Array new: 3.
trainings := 0.
input at: 1 put: 1. "Bias"]
randomizeSample
[| x y |
x := Random between: 0 and: 640-1.
y := Random between: 0 and: 360-1.
expected := (y >= (2*x+1)) ifTrue: [1] ifFalse: [-1].
input at: 2 put: x.
input at: 3 put: y]
test
[self
initializeTest; evaluate;
train: 1; evaluate;
train: 1; evaluate;
train: 1; evaluate;
train: 1; evaluate;
train: 1; evaluate;
train: 5; evaluate;
train: 10; evaluate;
train: 30; evaluate;
train: 50; evaluate;
train: 100; evaluate;
train: 300; evaluate;
train: 500; evaluate]
evaluate
[| hits |
hits := 0.
evaluationSamples timesRepeat:
[self randomizeSample.
expected = (perceptron feedForward: input)
ifTrue: [hits := hits + 1]].
Transcript
display: 'After ';
display: trainings;
display: ' trainings: ';
display: (hits / evaluationSamples * 100) asFloat;
display: ' % accuracy';
nl]
train: anInteger
[anInteger timesRepeat:
[self randomizeSample.
perceptron
train: input
desire: expected.
trainings := trainings + 1]]
]
Perceptron test.
Example output:
After 0 trainings: 14.158 % accuracy
After 1 trainings: 14.018 % accuracy
After 2 trainings: 14.19 % accuracy
After 3 trainings: 14.049 % accuracy
After 4 trainings: 14.029 % accuracy
After 5 trainings: 14.105 % accuracy
After 10 trainings: 20.39 % accuracy
After 20 trainings: 57.08 % accuracy
After 50 trainings: 92.998 % accuracy
After 100 trainings: 98.988 % accuracy
After 200 trainings: 98.055 % accuracy
After 500 trainings: 99.777 % accuracy
After 1000 trainings: 98.523 % accuracy
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.
(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)
{{out}}
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
{{trans|Java}} Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#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] }
}
}
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");
{{out}} [[File:Perceptron.zkl.jpg]]