A simple non-linear perceptron classifier

perceptron.m

LEARNING_RATE = 0.1;
MAX_ITERATIONS = 1e3;
MIN_ERROR = 1e-3;
%load input and target
perceptron_data;
[numInst, numDims] = size(input);
numClasses = size(target,2);
weights = randn(numClasses, 3*numDims);
isDone = false;
iter = 0;
while ~isDone
    iter = iter + 1;
    err = zeros(numInst,numClasses);
    for i=1:numInst
        output = ( weights * [1;input(i,:)' ;...
            ( input(i,1).*input(i,2) )' ; (input(i,:).^2)' ] >= 0 );
        err(i,:) = target(i,:)' - output;
        weights = weights + ...
            LEARNING_RATE * err(i,:)' * ...
            [1 input(i,:) input(i,1).*input(i,2) input(i,:).^2];
    end
    rmse = sqrt(sum(err.^2,1)/numInst);
    if ( iter >= MAX_ITERATIONS || all(rmse < MIN_ERROR) )
        isDone = true;
    end
end
[~,group] = max([target ~target],[],2);
gscatter(input(:,1), input(:,2), group), hold on
xLimits = get(gca,'xlim');
yLimits = get(gca,'ylim');
for i=1:numClasses
    ezplot(sprintf(...
        '%f + %f*x + %f*y + %f*x*y + %f*x.^2 + %f*y.^2', ...
        weights(i,:)), xLimits, yLimits)
end
title('Perceptron decision boundaries')
hold off

perceptron_data.m

% -------------------------------------------------------------------
%  Generated by MATLAB on 15-Apr-2019 00:52:40
%  MATLAB version: 9.5.0.944444 (R2018b)
% -------------------------------------------------------------------
                               

input = ...
  [-0.639 -0.574;
   -0.355 0.251;
   0.872 -0.024;
   -0.983 -0.108;
   -0.249 0.897;
   -0.589 0.128;
   0.662 0.266;
   0.224 0.85;
   -0.831 -0.527;
   0.614 0.095;
   0.028 0.319;
   0.158 -0.036;
   -0.545 -0.657;
   0.061 0.663;
   -0.363 -0.077;
   -0.016 0.584;
   0.544 0.057;
   0.036 -0.728;
   0 0.872;
   0.732 -0.254;
   -0.033 -0.132;
   -0.358 -0.691;
   -0.759 0.024;
   0.586 0.131;
   -0.552 0.488;
   0.552 0.337;
   0.612 -0.073;
   -0.076 0.008;
   -0.581 -0.569;
   0.45 -0.799;
   0.619 0.063;
   0.16 -0.728;
   0.292 -0.771;
   -0.857 0.351;
   -0.484 0.451;
   0.229 -0.592;
   -0.425 0.225;
   0.483 0.733;
   -0.579 0.717;
   0.152 -0.326;
   -0.671 -0.539;
   -0.595 -0.293;
   0.083 0.656;
   0.697 0.618;
   0.53 -0.205;
   -0.918 0.38;
   0.517 0.153;
   0.41 0.294;
   -0.976 0.009;
   -0.935 -0.084;
   -0.444 -0.366;
   0.337 0.683;
   0.063 -0.578;
   0.272 0.492;
   0.254 -0.356;
   0.22 -0.149;
   0.467 0.738;
   0.196 0.669;
   0.666 -0.245;
   0.109 -0.7;
   0.103 0.45;
   0.696 0.064;
   0.008 -0.393;
   0.187 0.714;
   0.971 -0.072;
   -0.317 0.259;
   0.37 0.249;
   0.437 -0.075;
   0.061 -0.192;
   -0.105 -0.89;
   0.78 0.502;
   -0.252 -0.613;
   -0.111 -0.796;
   -0.098 -0.58;
   -0.964 -0.244;
   -0.561 -0.317;
   0.868 0.231;
   0.245 0.447;
   0.353 0.514;
   -0.619 -0.221;
   0.213 0.113;
   0.114 0.277;
   0.013 0.783;
   0.748 0.233;
   0.583 -0.21;
   -0.519 -0.424;
   -0.042 0.219;
   -0.651 -0.368;
   -0.051 -0.759;
   0.391 0.798;
   0.825 -0.401;
   0.293 -0.302;
   0.729 0.257;
   0.046 -0.302;
   -0.109 0.023;
   0.279 -0.292;
   0.575 0.529;
   0.484 -0.764;
   -0.344 -0.293;
   0.743 -0.329];

target = [1; 0; 0; 1; 0; 0; 1; 1; 1; 1; 1; 0; 1; 1; 1; 0; 1; 0; 1; 0; 1; ...
          1; 0; 1; 0; 1; 0; 0; 1; 0; 1; 0; 0; 0; 0; 0; 0; 1; 0; 0; 1; 1; ...
          1; 1; 0; 0; 1; 1; 0; 1; 1; 1; 0; 1; 0; 0; 1; 1; 0; 0; 1; 1; 0; ...
          1; 0; 0; 1; 0; 0; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; ...
          0; 1; 0; 1; 1; 1; 0; 0; 1; 0; 0; 0; 1; 0; 1; 0];