Mathematica 教學 主成分分析

(*產生500組隨機變數*)
data=Block[{t},{#,3+#*0.2+RandomReal[NormalDistribution[0,1]]}&/@
Table[RandomReal[NormalDistribution[0,2]],{500}]];
Manipulate[
Block[{p1=point1,p2=point2,m,v1,myline,pp,pcadata,
pcaslope},
pcaslope=Divide@@Reverse@Eigensystem[Covariance[data]][[2,1]];
(*直線斜率*)
m=(p2[[2]]-p1[[2]])/(p2[[1]]-p1[[1]]);
(*計算投影座標*)
v1=point2-point1;
pcadata=p1+Projection[#-point1,v1]&/@data;
Column[{
"Variance="<>ToString[Variance[{p1-p2}.#&/@data][[1]]],
Plot[{m(x-p1[[1]])+p1[[2]],
pcaslope(x-p1[[1]])+p1[[2]]},{x,-20,20},
PlotStyle->{{Green,Thickness[0.01]},Automatic},
PlotRange->{{-10,10},{-7.5,12.5}},
Axes->False,Frame->True,AspectRatio->1,
Epilog->{Blue,PointSize[0.0125],Point[data],
Red,PointSize[0.025],Point[pcadata]},ImageSize->500]}]],
{{point1,{-1,-5}},Locator},{{point2,{2,1}},Locator}]

Tags: Mathematica 教學, Teaching

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