我正在审核Toronto perceptron MATLAB code
中的代码代码是
function [w] = perceptron(X,Y,w_init)
w = w_init;
for iteration = 1 : 100 %<- in practice, use some stopping criterion!
for ii = 1 : size(X,2) %cycle through training set
if sign(w'*X(:,ii)) ~= Y(ii) %wrong decision?
w = w + X(:,ii) * Y(ii); %then add (or subtract) this point to w
end
end
sum(sign(w'*X)~=Y)/size(X,2) %show misclassification rate
end
所以我正在阅读如何将此函数应用于数据矩阵X和目标Y，但是，不知道如何使用此函数，据我所知，它返回一个权重向量，因此它可以进行分类。
你能举个例子，解释一下吗？
我试过了
X=[0 0; 0 1; 1 1]
Y=[1 0; 2 1]
w=[1 1 1]
Result = perceptron( X, Y, w )
??? Error using ==> mtimes
Inner matrix dimensions must agree.
Error in ==> perceptron at 15
if sign(w'*X(:,ii)) ~= Y(ii)
Result = perceptron( X, Y, w' )
??? Error using ==> ne
Matrix dimensions must agree.
Error in ==> perceptron at 19
sum(sign(w'*X)~=Y) / size(X,2);
由于
谢谢你的回答，我还有一个，如果我改变Y = [0,1]，算法会发生什么？
那么，任何输入数据都不适用于Y = [0,1]这个感知器的代码对吗？
----------------------------- EDIT -------------- ----------
还有一个问题，如果我想绘制划分2个类的行，我知道我们可以得到解决线性方程系统的线，它与权重有关，但是如何， 我该怎么办？，我正在尝试像
这样的东西% the initial weights
w_init = [ 1 1 1]';
% the weights returned from perceptron
wtag = perceptron(X,Y,w_init,15);
% concatenate both
Line = [wtag,w_init]
% solve the linear system, am I correct doing this?
rref(Line')
% plot???
答案 0 :(得分：17)
您应该首先了解每个输入的含义：
X是大小为M x N的示例的输入矩阵，其中M是特征向量的维数，N是样本数。由于用于预测的感知器模型为Y=w*X+b，因此您必须在X中提供一个额外的维度，该维度是常量，通常设置为1，因此b术语是“已构建的” -in“进入X。在下面针对X的示例中，我将X的最后一个条目设置为所有样本中的1。Y是来自X（您希望感知器学习的分类）的每个样本的正确分类，因此它应该是N维行向量 - 每个输入示例的一个输出。由于感知器是二进制分类器，因此它应该只有2个不同的可能值。查看代码，您会看到它检查预测的符号，它告诉您允许的Y值应为-1,+1（例如，而不是0,1）。< / LI>
w是您要学习的权重向量。因此，尝试使用：
调用该函数X=[0 0; 0 1; 1 1];
Y=[1 -1];
w=[.5; .5; .5];
修改
使用以下代码调用perceptron alg并以图形方式查看结果：
% input samples
X1=[rand(1,100);rand(1,100);ones(1,100)]; % class '+1'
X2=[rand(1,100);1+rand(1,100);ones(1,100)]; % class '-1'
X=[X1,X2];
% output class [-1,+1];
Y=[-ones(1,100),ones(1,100)];
% init weigth vector
w=[.5 .5 .5]';
% call perceptron
wtag=perceptron(X,Y,w);
% predict
ytag=wtag'*X;
% plot prediction over origianl data
figure;hold on
plot(X1(1,:),X1(2,:),'b.')
plot(X2(1,:),X2(2,:),'r.')
plot(X(1,ytag<0),X(2,ytag<0),'bo')
plot(X(1,ytag>0),X(2,ytag>0),'ro')
legend('class -1','class +1','pred -1','pred +1')
答案 1 :(得分：10)
如果您有兴趣，这里有一个以相当教程的方式编写的小型感知器演示：
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 > 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 & 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 > 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 & 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 ) ) ...
&& 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 > 0;
isNegativeClass = Data.labels <= 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
答案 2 :(得分：1)
试试这个：
perceptron([1 2 1 2], [1 0 1 0], 0.5);