PCA

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(Example and Mathematical Background)
(Rotating the Data)
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<math>\textstyle x_{\rm rot}^{(i)} = U^Tx^{(i)}</math> for every <math>\textstyle i</math>.  Plotting this transformed data  
<math>\textstyle x_{\rm rot}^{(i)} = U^Tx^{(i)}</math> for every <math>\textstyle i</math>.  Plotting this transformed data  
<math>\textstyle x_{\rm rot}</math>, we get:  
<math>\textstyle x_{\rm rot}</math>, we get:  
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\begin{center}
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\includegraphics[width=0.6\maxfigwidth]{PCA-rotated.png}
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INSERT GRAPHIC HERE
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\vspace*{-0.2in}
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\end{center}
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This is the training set rotated into the <math>\textstyle u_1</math>,<math>\textstyle u_2</math> basis. In the general
This is the training set rotated into the <math>\textstyle u_1</math>,<math>\textstyle u_2</math> basis. In the general
case, <math>\textstyle U^Tx</math> will be the training set rotated into the basis  
case, <math>\textstyle U^Tx</math> will be the training set rotated into the basis  

Revision as of 05:29, 2 April 2011

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