view applet and source

Long overdue, I’ve started working on a series of examples that implement neural networks. First up is the simplest, a little Perceptron that learns whether points live on one side of a line (in Cartesian space) or the other.

y = x*0.9-0.2

In this example, the perceptron is trained via an array of known point objects (with known answers), and the resulting “guess” line is displayed in real-time. I made the learning constant rather low so that one can see the slow progression of changing weights. I’ve been spending some quality time with Artifical Intelligence, by George Luger. It’s a wonderful book, and even better, it’s free for download online!

All the code is in the link, but here’s a quick peek at the meat of the matter: a function inside the Perceptron class that adjusts weights according to 3 input values and their corresponding “known” output. (Note if the perceptron’s guess output produces the desired result, the weights are not changed.)

A more involved write-up will arrive online at some point. . .

// Function to train the Perceptron
// Weights are adjusted based on "desired" answer
void train(float[] vals, int desired) {
  // Sum all the weights
  float sum = 0;
  for (int i = 0; i < weights.length; i++) {
    sum += vals[i]*weights[i];
  }
  // The result is the sign of the sum
  int result = 1;  // Start with 1
  if (sum < 0) result = -1; // If less than zero, change to -1
  // Compute factor to change weight
  // (DESIRED - RESULT): note this can only be 0, -2, or 2
  // Multiply by learning constant
  float weightChange = c*(desired - result);
  // Adjust weights based on weightChange * input
  for (int i = 0; i < weights.length; i++) {
    weights[i] += weightChange * vals[i];         
  }
}

For related work, check out Aaron Steed’s site.