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How to generate polynomial matrix in classification problems ?

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Abdelwahab Afifi
Abdelwahab Afifi on 18 Mar 2020
Edited: Abdelwahab Afifi on 20 Mar 2020
I have the fllowing samples [1 2] , [2 0] , [1 1], [3 1], [2 3], [3 3] which correspond to labels y : {0, 0, 0, 1, 1, 1} respectively. Our goal is to predict the class label of xt1=[4 1] and xt2=[1 0] .
I already simulate the 3) MSE using indicator Matrix as follow:
clc; clear all; close all;
s1=[1 2];
s2=[2 0];
s3=[1 1];
s4=[3 1];
s5=[2 3];
s6=[3 3];
S=[s1;s2;s3;s4;s5;s6];
xt1=[4 1];
xt2=[1 0];
disp('MSE using Indicator Matrix (Primal)')
X=Xo
Y=[ones(3,1) zeros(3,1);zeros(3,1) ones(3,1)]
w=inv(X'*X)*X'*Y
predict1=[1 xt1]*w
predict2=[1 xt2]*w
predict=[1 xt1; 1 xt2]*w
However, in case of MSE with polynomial, how can I calculate matrix P in case of 2'nd order and 3'rd order polynomial ?! to get the same results. I tried the following code, but can't obtain the same results.
% MSE with Polynomial (Dual)
X=[ones(6,1) S S.^2 S(:,1).*S(:,2)]
Y=[ones(3,1) zeros(3,1);zeros(3,1) ones(3,1)]
w=X'*inv(X*X')*Y % Dual
predict1=[1 xt1 xt1.^2 xt1(1)*xt1(2)]*w
predict1=[1 xt2 xt2.^2 xt2(1)*xt2(2)]*w

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