Perceptron: Difference between revisions
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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 [[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. |
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A perceptron attempts to |
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. |
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In order for the perceptron to make the right decision, it |
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. |
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Revision as of 22:12, 25 April 2016
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.
- The 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 print an image of the result.
- See also
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(30, (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);
int x = getWidth(); int y = (int) f(x); g.setStroke(new BasicStroke(2)); g.setColor(Color.orange); g.drawLine(0, 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); }); }