PLA: Let share nice visualizations

[vakhov]

Hi!

I think all of us plotted different pictures. Some of them are very nice. For example I get this for PLA learning on N=20. What nice visualisations do you have?

[Yann222]

I don't think it's sharing answers to homework if we exchange code for plotting. Am new to Octave and not having the best luck getting nice-looking plots so far. Would be thrilled to get just the snippet of code people use for visualizing different solutions.

[Anne Paulson]

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.

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

[chocobo_rider]

Wow, nice figure. I didn't visualize it like that. I chose to make an animation of the process

[vikram360]

Please, good sir, do share it

[theTB]

Here is a visualization of the algorithm with n=50 points. The point in the circle is the chosen misclassified point in the current iteration. The final yellow line is the selected hypothesis.

[yaser]

Originally Posted by theTB

Here is a visualization of the algorithm with n=50 points.

Cool.

[gah44]

I never did any plots.

I did a few drawings with a few points on them to understand the geometry, and once I understood that, believed in the equations.

But sometimes plots are nice to see what it is really doing.

[Yann222]

Thanks Anne for sharing your code. Helped me pick up a few things that I was able to use to produce my own plots.

[Barath]