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#3
 Anne Paulson Senior Member Join Date: Jan 2013 Location: Silicon Valley Posts: 52 Re: PLA: Let share nice visualizations

I'm just going to paste the Octave code right here. Hope that's OK.

This is code to display the current state of the perceptron, displaying the true separating line, the current hypothesis and all the points. Wrongly classified points are big; rightly classified points are little. Optionally, you can specify the new hypothesis and the currently selected misclassified point, and then they too will be displayed.

When I call this function, I put a pause statement afterwards, so I can step through the algorithm watching it move the hypothesis line and reclassify all the points.

For some reason I'm getting a divide by zero warning for the statements with && in them. I ignore it.

Code:
```function draw_percept(points,hypothesis, predictions, true_line, target, bad, new_h)

# points (number of points, weights) is the data points. the bias weight is LAST
# hypothesis is the hypothesis. bias term is LAST.
# predictions(1, N) is what the hypothesis predicts for the points.
# true_line is the true separating line. bias term is LAST
# target is the correct classifications for the points
# bad is optional; it's the misclassified point
# new_h is optional; it's the new hypothesis

[hypx hypy] = pts_from_hypothesis(hypothesis);
[truex truey] = pts_from_hypothesis(true_line);

rightly_on = find(predictions == target & predictions == 1);
wrongly_on = find(predictions != target & predictions ==1);
rightly_off = find(predictions == target & predictions == -1);
wrongly_off = find(predictions!= target & predictions == -1);

hold off;
# if we are displaying old & new hypotheses,
# display true line, old hypothesis, new hypothesis
if nargin >6
[newx newy] = pts_from_hypothesis(new_h);
plot(hypx, hypy, 'r', truex, truey,'g',newx, newy,':b');
legend("old hypothesis red", "true line green", "new hypothesis blue", "location", "southeast");
else
# otherwise plot the hypothesis & real line
plot(hypx, hypy, 'r', truex, truey,'g');
legend("old hypothesis", "new hypothesis", "location", "southeast");
end

axis([-1 1 -1 1]);

hold on;
title("Perceptron");

# plot the points
scatter(points(rightly_on, 1),points(rightly_on, 2), 'g');
hold on;
scatter(points(rightly_off, 1),points(rightly_off, 2), 'b');
hold on;
scatter(points(wrongly_on, 1),points(wrongly_on, 2),15, 'r');
hold on;
scatter(points(wrongly_off, 1),points(wrongly_off, 2),15,  'c');

# if we're displaying the selected bad point, display it
if nargin >3
hold on;
scatter(bad(1), bad(2), 20, 'b');
end
end

function [xs ys] = pts_from_hypothesis(hypothesis)
# hypothesis is a, b, c where line is ax + by + c> 0

# so y = -(a/b)x - c/b
# and x =-(b/a)y - c/a

# we need to find the the intercepts for y=-1, x=-1, y=1 and
# x = 1. Two of those points will be in the [-1,1],[-1,1] box

a = hypothesis(1);
b = hypothesis(2);
c= hypothesis(3);
xm1int = (b-c)/a;
ym1int = (a-c)/b;
x1int = (-b-c)/a;
y1int = (-a-c)/b;

xs = [-1 1 xm1int x1int];
ys = [ym1int y1int -1 1];

end```