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Added programming exercise 1 (Week 3)

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Matthias Neeracher 2017-01-01 22:36:27 +01:00
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NNML1/dataset1.mat Normal file
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NNML1/learn_perceptron.m Normal file
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%% 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

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%% Plots information about a perceptron classifier on a 2-dimensional dataset.
function plot_perceptron(neg_examples, pos_examples, mistakes0, mistakes1, num_err_history, w, w_dist_history)
%%
% The top-left plot shows the dataset and the classification boundary given by
% the weights of the perceptron. The negative examples are shown as circles
% while the positive examples are shown as squares. If an example is colored
% green then it means that the example has been correctly classified by the
% provided weights. If it is colored red then it has been incorrectly classified.
% The top-right plot shows the number of mistakes the perceptron algorithm has
% made in each iteration so far.
% The bottom-left plot shows the distance to some generously feasible weight
% vector if one has been provided (note, there can be an infinite number of these).
% Points that the classifier has made a mistake on are shown in red,
% while points that are correctly classified are shown in green.
% The goal is for all of the points to be green (if it is possible to do so).
% 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.
% mistakes0 - A vector containing the indices of the datapoints from class 0 incorrectly
% classified by the perceptron. This is a subset of neg_examples.
% mistakes1 - A vector containing the indices of the datapoints from class 1 incorrectly
% classified by the perceptron. This is a subset of pos_examples.
% num_err_history - A vector containing the number of mistakes for each
% iteration of learning so far.
% w - A 3-dimensional vector corresponding to the current weights of the
% perceptron. The last element is the bias.
% w_dist_history - A vector containing the L2-distance to a generously
% feasible weight vector for each iteration of learning so far.
% Empty if one has not been provided.
%%
f = figure(1);
clf(f);
neg_correct_ind = setdiff(1:size(neg_examples,1),mistakes0);
pos_correct_ind = setdiff(1:size(pos_examples,1),mistakes1);
subplot(2,2,1);
hold on;
if (~isempty(neg_examples))
plot(neg_examples(neg_correct_ind,1),neg_examples(neg_correct_ind,2),'og','markersize',20);
end
if (~isempty(pos_examples))
plot(pos_examples(pos_correct_ind,1),pos_examples(pos_correct_ind,2),'sg','markersize',20);
end
if (size(mistakes0,1) > 0)
plot(neg_examples(mistakes0,1),neg_examples(mistakes0,2),'or','markersize',20);
end
if (size(mistakes1,1) > 0)
plot(pos_examples(mistakes1,1),pos_examples(mistakes1,2),'sr','markersize',20);
end
title('Classifier');
%In order to plot the decision line, we just need to get two points.
plot([-5,5],[(-w(end)+5*w(1))/w(2),(-w(end)-5*w(1))/w(2)],'k')
xlim([-1,1]);
ylim([-1,1]);
hold off;
subplot(2,2,2);
plot(0:length(num_err_history)-1,num_err_history);
xlim([-1,max(15,length(num_err_history))]);
ylim([0,size(neg_examples,1)+size(pos_examples,1)+1]);
title('Number of errors');
xlabel('Iteration');
ylabel('Number of errors');
subplot(2,2,3);
plot(0:length(w_dist_history)-1,w_dist_history);
xlim([-1,max(15,length(num_err_history))]);
ylim([0,15]);
title('Distance')
xlabel('Iteration');
ylabel('Distance');