NNML/NNML1/learn_perceptron.m

%% Learns the weights of a perceptron and displays the results.
function [w] = learn_perceptron(neg_examples_nobias,pos_examples_nobias,w_init,w_gen_feas)
%% 
% Learns the weights of a perceptron for a 2-dimensional dataset and plots
% the perceptron at each iteration where an iteration is defined as one
% full pass through the data. If a generously feasible weight vector
% is provided then the visualization will also show the distance
% of the learned weight vectors to the generously feasible weight vector.
% Required Inputs:
%   neg_examples_nobias - The num_neg_examples x 2 matrix for the examples with target 0.
%       num_neg_examples is the number of examples for the negative class.
%   pos_examples_nobias - The num_pos_examples x 2 matrix for the examples with target 1.
%       num_pos_examples is the number of examples for the positive class.
%   w_init - A 3-dimensional initial weight vector. The last element is the bias.
%   w_gen_feas - A generously feasible weight vector.
% Returns:
%   w - The learned weight vector.
%%

%Bookkeeping
num_neg_examples = size(neg_examples_nobias,1);
num_pos_examples = size(pos_examples_nobias,1);
num_err_history = [];
w_dist_history = [];

%Here we add a column of ones to the examples in order to allow us to learn
%bias parameters.
neg_examples = [neg_examples_nobias,ones(num_neg_examples,1)];
pos_examples = [pos_examples_nobias,ones(num_pos_examples,1)];

%If weight vectors have not been provided, initialize them appropriately.
if (~exist('w_init','var') || isempty(w_init))
    w = randn(3,1);
else
    w = w_init;
end

if (~exist('w_gen_feas','var'))
    w_gen_feas = [];
end

%Find the data points that the perceptron has incorrectly classified
%and record the number of errors it makes.
iter = 0;
[mistakes0, mistakes1] = eval_perceptron(neg_examples,pos_examples,w);
num_errs = size(mistakes0,1) + size(mistakes1,1);
num_err_history(end+1) = num_errs;
fprintf('Number of errors in iteration %d:\t%d\n',iter,num_errs);
fprintf(['weights:\t', mat2str(w), '\n']);
plot_perceptron(neg_examples, pos_examples, mistakes0, mistakes1, num_err_history, w, w_dist_history);
key = input('<Press enter to continue, q to quit.>', 's');
if (key == 'q')
    return;
end

%If a generously feasible weight vector exists, record the distance
%to it from the initial weight vector.
if (length(w_gen_feas) ~= 0)
    w_dist_history(end+1) = norm(w - w_gen_feas);
end

%Iterate until the perceptron has correctly classified all points.
while (num_errs > 0)
    iter = iter + 1;

    %Update the weights of the perceptron.
    w = update_weights(neg_examples,pos_examples,w);

    %If a generously feasible weight vector exists, record the distance
    %to it from the current weight vector.
    if (length(w_gen_feas) ~= 0)
        w_dist_history(end+1) = norm(w - w_gen_feas);
    end

    %Find the data points that the perceptron has incorrectly classified.
    %and record the number of errors it makes.
    [mistakes0, mistakes1] = eval_perceptron(neg_examples,pos_examples,w);
    num_errs = size(mistakes0,1) + size(mistakes1,1);
    num_err_history(end+1) = num_errs;

    fprintf('Number of errors in iteration %d:\t%d\n',iter,num_errs);
    fprintf(['weights:\t', mat2str(w), '\n']);
    plot_perceptron(neg_examples, pos_examples, mistakes0, mistakes1, num_err_history, w, w_dist_history);
    key = input('<Press enter to continue, q to quit.>', 's');
    if (key == 'q')
        break;
    end
end

%WRITE THE CODE TO COMPLETE THIS FUNCTION
function [w] = update_weights(neg_examples, pos_examples, w_current)
%% 
% Updates the weights of the perceptron for incorrectly classified points
% using the perceptron update algorithm. This function makes one sweep
% over the dataset.
% Inputs:
%   neg_examples - The num_neg_examples x 3 matrix for the examples with target 0.
%       num_neg_examples is the number of examples for the negative class.
%   pos_examples- The num_pos_examples x 3 matrix for the examples with target 1.
%       num_pos_examples is the number of examples for the positive class.
%   w_current - A 3-dimensional weight vector, the last element is the bias.
% Returns:
%   w - The weight vector after one pass through the dataset using the perceptron
%       learning rule.
%%
w = w_current;
num_neg_examples = size(neg_examples,1);
num_pos_examples = size(pos_examples,1);
for i=1:num_neg_examples
    this_case = neg_examples(i,:);
    x = this_case'; %Hint
    activation = this_case*w;
    if (activation >= 0)
        w = w-x
    end
end
for i=1:num_pos_examples
    this_case = pos_examples(i,:);
    x = this_case';
    activation = this_case*w;
    if (activation < 0)
        w = w+x
    end
end

function [mistakes0, mistakes1] =  eval_perceptron(neg_examples, pos_examples, w)
%% 
% Evaluates the perceptron using a given weight vector. Here, evaluation
% refers to finding the data points that the perceptron incorrectly classifies.
% Inputs:
%   neg_examples - The num_neg_examples x 3 matrix for the examples with target 0.
%       num_neg_examples is the number of examples for the negative class.
%   pos_examples- The num_pos_examples x 3 matrix for the examples with target 1.
%       num_pos_examples is the number of examples for the positive class.
%   w - A 3-dimensional weight vector, the last element is the bias.
% Returns:
%   mistakes0 - A vector containing the indices of the negative examples that have been
%       incorrectly classified as positive.
%   mistakes0 - A vector containing the indices of the positive examples that have been
%       incorrectly classified as negative.
%%
num_neg_examples = size(neg_examples,1);
num_pos_examples = size(pos_examples,1);
mistakes0 = [];
mistakes1 = [];
for i=1:num_neg_examples
    x = neg_examples(i,:)';
    activation = x'*w;
    if (activation >= 0)
        mistakes0 = [mistakes0;i];
    end
end
for i=1:num_pos_examples
    x = pos_examples(i,:)';
    activation = x'*w;
    if (activation < 0)
        mistakes1 = [mistakes1;i];
    end
end