Added programming exercise 1 (Week 3)
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Matthias Neeracher
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ec7434e9a1
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NNML1/dataset1.mat
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NNML1/dataset1.mat
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NNML1/dataset2.mat
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NNML1/dataset2.mat
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NNML1/dataset3.mat
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NNML1/dataset3.mat
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NNML1/dataset4.mat
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NNML1/dataset4.mat
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NNML1/learn_perceptron.m
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NNML1/learn_perceptron.m
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%% Learns the weights of a perceptron and displays the results.
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function [w] = learn_perceptron(neg_examples_nobias,pos_examples_nobias,w_init,w_gen_feas)
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%%
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% Learns the weights of a perceptron for a 2-dimensional dataset and plots
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% the perceptron at each iteration where an iteration is defined as one
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% full pass through the data. If a generously feasible weight vector
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% is provided then the visualization will also show the distance
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% of the learned weight vectors to the generously feasible weight vector.
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% Required Inputs:
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% neg_examples_nobias - The num_neg_examples x 2 matrix for the examples with target 0.
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% num_neg_examples is the number of examples for the negative class.
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% pos_examples_nobias - The num_pos_examples x 2 matrix for the examples with target 1.
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% num_pos_examples is the number of examples for the positive class.
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% w_init - A 3-dimensional initial weight vector. The last element is the bias.
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% w_gen_feas - A generously feasible weight vector.
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% Returns:
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% w - The learned weight vector.
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%%
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%Bookkeeping
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num_neg_examples = size(neg_examples_nobias,1);
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num_pos_examples = size(pos_examples_nobias,1);
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num_err_history = [];
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w_dist_history = [];
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%Here we add a column of ones to the examples in order to allow us to learn
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%bias parameters.
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neg_examples = [neg_examples_nobias,ones(num_neg_examples,1)];
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pos_examples = [pos_examples_nobias,ones(num_pos_examples,1)];
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%If weight vectors have not been provided, initialize them appropriately.
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if (~exist('w_init','var') || isempty(w_init))
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w = randn(3,1);
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else
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w = w_init;
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end
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if (~exist('w_gen_feas','var'))
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w_gen_feas = [];
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end
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%Find the data points that the perceptron has incorrectly classified
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%and record the number of errors it makes.
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iter = 0;
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[mistakes0, mistakes1] = eval_perceptron(neg_examples,pos_examples,w);
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num_errs = size(mistakes0,1) + size(mistakes1,1);
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num_err_history(end+1) = num_errs;
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fprintf('Number of errors in iteration %d:\t%d\n',iter,num_errs);
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fprintf(['weights:\t', mat2str(w), '\n']);
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plot_perceptron(neg_examples, pos_examples, mistakes0, mistakes1, num_err_history, w, w_dist_history);
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key = input('<Press enter to continue, q to quit.>', 's');
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if (key == 'q')
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return;
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end
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%If a generously feasible weight vector exists, record the distance
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%to it from the initial weight vector.
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if (length(w_gen_feas) ~= 0)
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w_dist_history(end+1) = norm(w - w_gen_feas);
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end
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%Iterate until the perceptron has correctly classified all points.
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while (num_errs > 0)
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iter = iter + 1;
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%Update the weights of the perceptron.
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w = update_weights(neg_examples,pos_examples,w);
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%If a generously feasible weight vector exists, record the distance
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%to it from the current weight vector.
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if (length(w_gen_feas) ~= 0)
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w_dist_history(end+1) = norm(w - w_gen_feas);
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end
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%Find the data points that the perceptron has incorrectly classified.
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%and record the number of errors it makes.
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[mistakes0, mistakes1] = eval_perceptron(neg_examples,pos_examples,w);
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num_errs = size(mistakes0,1) + size(mistakes1,1);
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num_err_history(end+1) = num_errs;
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fprintf('Number of errors in iteration %d:\t%d\n',iter,num_errs);
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fprintf(['weights:\t', mat2str(w), '\n']);
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plot_perceptron(neg_examples, pos_examples, mistakes0, mistakes1, num_err_history, w, w_dist_history);
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key = input('<Press enter to continue, q to quit.>', 's');
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if (key == 'q')
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break;
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end
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end
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%WRITE THE CODE TO COMPLETE THIS FUNCTION
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function [w] = update_weights(neg_examples, pos_examples, w_current)
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%%
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% Updates the weights of the perceptron for incorrectly classified points
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% using the perceptron update algorithm. This function makes one sweep
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% over the dataset.
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% Inputs:
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% neg_examples - The num_neg_examples x 3 matrix for the examples with target 0.
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% num_neg_examples is the number of examples for the negative class.
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% pos_examples- The num_pos_examples x 3 matrix for the examples with target 1.
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% num_pos_examples is the number of examples for the positive class.
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% w_current - A 3-dimensional weight vector, the last element is the bias.
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% Returns:
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% w - The weight vector after one pass through the dataset using the perceptron
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% learning rule.
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%%
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w = w_current;
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num_neg_examples = size(neg_examples,1);
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num_pos_examples = size(pos_examples,1);
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for i=1:num_neg_examples
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this_case = neg_examples(i,:);
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x = this_case'; %Hint
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activation = this_case*w;
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if (activation >= 0)
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w = w-x
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end
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end
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for i=1:num_pos_examples
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this_case = pos_examples(i,:);
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x = this_case';
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activation = this_case*w;
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if (activation < 0)
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w = w+x
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end
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end
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function [mistakes0, mistakes1] = eval_perceptron(neg_examples, pos_examples, w)
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%%
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% Evaluates the perceptron using a given weight vector. Here, evaluation
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% refers to finding the data points that the perceptron incorrectly classifies.
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% Inputs:
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% neg_examples - The num_neg_examples x 3 matrix for the examples with target 0.
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% num_neg_examples is the number of examples for the negative class.
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% pos_examples- The num_pos_examples x 3 matrix for the examples with target 1.
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% num_pos_examples is the number of examples for the positive class.
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% w - A 3-dimensional weight vector, the last element is the bias.
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% Returns:
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% mistakes0 - A vector containing the indices of the negative examples that have been
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% incorrectly classified as positive.
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% mistakes0 - A vector containing the indices of the positive examples that have been
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% incorrectly classified as negative.
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%%
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num_neg_examples = size(neg_examples,1);
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num_pos_examples = size(pos_examples,1);
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mistakes0 = [];
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mistakes1 = [];
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for i=1:num_neg_examples
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x = neg_examples(i,:)';
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activation = x'*w;
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if (activation >= 0)
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mistakes0 = [mistakes0;i];
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end
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end
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for i=1:num_pos_examples
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x = pos_examples(i,:)';
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activation = x'*w;
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if (activation < 0)
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mistakes1 = [mistakes1;i];
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end
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end
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NNML1/plot_perceptron.m
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NNML1/plot_perceptron.m
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%% Plots information about a perceptron classifier on a 2-dimensional dataset.
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function plot_perceptron(neg_examples, pos_examples, mistakes0, mistakes1, num_err_history, w, w_dist_history)
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%%
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% The top-left plot shows the dataset and the classification boundary given by
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% the weights of the perceptron. The negative examples are shown as circles
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% while the positive examples are shown as squares. If an example is colored
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% green then it means that the example has been correctly classified by the
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% provided weights. If it is colored red then it has been incorrectly classified.
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% The top-right plot shows the number of mistakes the perceptron algorithm has
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% made in each iteration so far.
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% The bottom-left plot shows the distance to some generously feasible weight
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% vector if one has been provided (note, there can be an infinite number of these).
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% Points that the classifier has made a mistake on are shown in red,
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% while points that are correctly classified are shown in green.
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% The goal is for all of the points to be green (if it is possible to do so).
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% Inputs:
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% neg_examples - The num_neg_examples x 3 matrix for the examples with target 0.
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% num_neg_examples is the number of examples for the negative class.
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% pos_examples- The num_pos_examples x 3 matrix for the examples with target 1.
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% num_pos_examples is the number of examples for the positive class.
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% mistakes0 - A vector containing the indices of the datapoints from class 0 incorrectly
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% classified by the perceptron. This is a subset of neg_examples.
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% mistakes1 - A vector containing the indices of the datapoints from class 1 incorrectly
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% classified by the perceptron. This is a subset of pos_examples.
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% num_err_history - A vector containing the number of mistakes for each
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% iteration of learning so far.
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% w - A 3-dimensional vector corresponding to the current weights of the
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% perceptron. The last element is the bias.
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% w_dist_history - A vector containing the L2-distance to a generously
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% feasible weight vector for each iteration of learning so far.
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% Empty if one has not been provided.
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%%
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f = figure(1);
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clf(f);
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neg_correct_ind = setdiff(1:size(neg_examples,1),mistakes0);
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pos_correct_ind = setdiff(1:size(pos_examples,1),mistakes1);
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subplot(2,2,1);
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hold on;
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if (~isempty(neg_examples))
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plot(neg_examples(neg_correct_ind,1),neg_examples(neg_correct_ind,2),'og','markersize',20);
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end
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if (~isempty(pos_examples))
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plot(pos_examples(pos_correct_ind,1),pos_examples(pos_correct_ind,2),'sg','markersize',20);
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end
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if (size(mistakes0,1) > 0)
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plot(neg_examples(mistakes0,1),neg_examples(mistakes0,2),'or','markersize',20);
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end
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if (size(mistakes1,1) > 0)
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plot(pos_examples(mistakes1,1),pos_examples(mistakes1,2),'sr','markersize',20);
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end
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title('Classifier');
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%In order to plot the decision line, we just need to get two points.
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plot([-5,5],[(-w(end)+5*w(1))/w(2),(-w(end)-5*w(1))/w(2)],'k')
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xlim([-1,1]);
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ylim([-1,1]);
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hold off;
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subplot(2,2,2);
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plot(0:length(num_err_history)-1,num_err_history);
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xlim([-1,max(15,length(num_err_history))]);
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ylim([0,size(neg_examples,1)+size(pos_examples,1)+1]);
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title('Number of errors');
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xlabel('Iteration');
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ylabel('Number of errors');
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subplot(2,2,3);
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plot(0:length(w_dist_history)-1,w_dist_history);
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xlim([-1,max(15,length(num_err_history))]);
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ylim([0,15]);
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title('Distance')
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xlabel('Iteration');
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ylabel('Distance');
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