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    <p>If you are interested, here is a little perceptron demo written in quite a tutorial manner:</p> <pre><code>function perceptronDemo %PERCEPTRONDEMO % % A simple demonstration of the perceptron algorithm for training % a linear classifier, made as readable as possible for tutorial % purposes. It is derived from the treatment of linear learning % machines presented in Chapter 2 of "An Introduction to Support % Vector Machines" by Nello Cristianini and John Shawe-Taylor. % % Data = createTrainingData; Model = trainPerceptron( Data ); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function Model = trainPerceptron( Data ) %TRAINPERCEPTRON DOWN = 1; ACROSS = 2; assert( isequal( unique( Data.labels ), [-1; +1] ), ... 'Labels must be -1 or +1' ); % --------------------------------------------------------------------- % Normalise the data by calculating z-scores % % This makes plotting easier, but is not needed by the algorithm. % sampleMean = mean( Data.samples ); sampleStdDev = std( Data.samples ); Data.samples = bsxfun( @minus, Data.samples, sampleMean ); Data.samples = bsxfun( @rdivide, Data.samples, sampleStdDev ); % --------------------------------------------------------------------- % Calculate the squared radius of the smallest ball that encloses the % data and is centred on the origin. This is used to provide an % appropriate range and step size when updating the threshold (bias) % parameter. % sampleSize = size( Data.samples, DOWN ); maxNorm = realmin; for iObservation = 1:sampleSize observationNorm = norm( Data.samples(iObservation,:) ); if observationNorm &gt; maxNorm maxNorm = observationNorm; end end enclosingBallRadius = maxNorm; enclosingBallRadiusSquared = enclosingBallRadius .^ 2; % --------------------------------------------------------------------- % Define the starting weight vector and bias. These should be zeros, % as the algorithm omits a learning rate, and it is suggested in % Cristianini &amp; Shawe-Taylor that learning rate may only be omitted % safely when the starting weight vector and bias are zero. % Model.weights = [0.0 0.0]; Model.bias = 0.0; % --------------------------------------------------------------------- % Run the perceptron training algorithm % % To prevent program running forever when nonseparable data are % provided, limit the number of steps in the outer loop. % maxNumSteps = 1000; for iStep = 1:maxNumSteps isAnyObsMisclassified = false; for iObservation = 1:sampleSize; inputObservation = Data.samples( iObservation, : ); desiredLabel = Data.labels( iObservation ); % +1 or -1 perceptronOutput = sum( Model.weights .* inputObservation, ACROSS ) + Model.bias; margin = desiredLabel * perceptronOutput; isCorrectLabel = margin &gt; 0; % ------------------------------------------------------------- % If the model misclassifies the observation, update the % weights and the bias. % if ~isCorrectLabel isAnyObsMisclassified = true; weightCorrection = desiredLabel * inputObservation; Model.weights = Model.weights + weightCorrection; biasCorrection = desiredLabel .* enclosingBallRadiusSquared; Model.bias = Model.bias + biasCorrection; displayPerceptronState( Data, Model ); end % if this observation misclassified. end % loop over observations if ~isAnyObsMisclassified disp( 'Done!' ); break; end end % outer loop end % TRAINPERCEPTRON %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function Data = createTrainingData %CREATETRAININGDATA % % Return a structure containing training data suitable for linear % classification. % sampleAsize = 1024; sampleBsize = 1024; sampleAmean = [ 5.5 5.0 ]; sampleAstdDev = [ 0.5 1.0 ]; sampleBmean = [ 2.5 3.0 ]; sampleBstdDev = [ 0.3 0.7 ]; Data.samples = [ normallyDistributedSample( sampleAsize, sampleAmean, sampleAstdDev ); ... normallyDistributedSample( sampleBsize, sampleBmean, sampleBstdDev ) ]; Data.labels = [ ones(sampleAsize,1); ... -ones(sampleBsize,1) ]; % --------------------------------------------------------------------- % Randomly permute samples &amp; class labels. % % This is not really necessary, but done to illustrate that the order % in which observations are evaluated does not matter. % randomOrder = randperm( sampleAsize + sampleBsize ); Data.samples = Data.samples( randomOrder, : ); Data.labels = Data.labels( randomOrder, : ); end % CREATETRAININGDATA %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function samples = normallyDistributedSample( sampleSize, sampleMean, sampleStdDev ) %NORMALDISTRIBUTIONSAMPLE % % Draw a sample from a normal distribution with specified mean and % standard deviation. % assert( isequal( size( sampleMean ), size( sampleStdDev ) ) ... &amp;&amp; 1 == size( sampleMean, 1 ), ... 'Sample mean and standard deviation must be row vectors of equal length.' ); numFeatures = numel( sampleMean ); samples = randn( sampleSize, numFeatures ); samples = bsxfun( @times, samples, sampleStdDev ); samples = bsxfun( @plus, samples, sampleMean ); end % NORMALDISTRIBUTIONSAMPLE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function displayPerceptronState( Data, Model ) %DISPLAYPERCEPTRONSTATE hFig = figure( 1 ); clf; set( hFig, ... 'NumberTitle', 'off', ... 'Name', mfilename, ... 'MenuBar', 'none', ... 'Color', [1.0 1.0 1.0] ); displayXmin = -4; displayXmax = 4; displayYmin = -4; displayYmax = 4; hAx = subplot( 1, 1, 1 ); axis('equal'); set( hAx, ... 'Box', 'on', ... 'NextPlot', 'add', ... 'xgrid', 'on', ... 'ygrid', 'on', ... 'xlim', [displayXmin displayXmax], ... % Bounds suitable for Z-scored data 'ylim', [displayYmin displayYmax] ); xlabel( 'x_1' ); ylabel( 'x_2' ); % --------------------------------------------------------------------- % Plot data points from the two classes % isPositiveClass = Data.labels &gt; 0; isNegativeClass = Data.labels &lt;= 0; plot( hAx, Data.samples(isPositiveClass,1), Data.samples(isPositiveClass,2), 'b+' ); plot( hAx, Data.samples(isNegativeClass,1), Data.samples(isNegativeClass,2), 'rx' ); % --------------------------------------------------------------------- % Display parameters for separating hyperplane in title % xWeight = Model.weights(1); yWeight = Model.weights(2); bias = Model.bias; szTitle = sprintf( 'Linear classifier parameters: %0.2f x_1 + %0.2f x_2 + %0.2f = 0', xWeight, yWeight, bias ); title( szTitle ); % --------------------------------------------------------------------- % Plot separating hyperplane % y1 = ( (xWeight*displayXmin) + bias ) ./ -yWeight; y2 = ( (xWeight*displayXmax) + bias ) ./ -yWeight; plot( hAx, [displayXmin; displayXmax], [y1, y2], 'k-', 'linewidth', 2 ); pause(0.1); end % DISPLAYPERCEPTRONSTATE </code></pre>
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    1. POImplementing and ploting a perceptron in MATLAB
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    1. USWilliam Payne
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