Principal Component Analysis (PCA)
Principal Component Analysis (PCA)
Principal Component Analysis (PCA)
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Maximum Variance Projection<br />
• Consider a random vector x with arbitrary joint pdf<br />
• in <strong>PCA</strong> we assume that x has zero mean<br />
• we can always achieve this by constructing x’=x-µ<br />
• Scatter plot and projection y onto a “weight” vector w<br />
w<br />
y<br />
n<br />
T<br />
= w x = ∑<br />
i=<br />
1<br />
cos(<br />
α )<br />
• Motivating question: y is a scalar random variable that<br />
depends on w; for which w is the variance of y maximal?<br />
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 2<br />
x<br />
y<br />
=<br />
w<br />
×<br />
x<br />
×<br />
w<br />
i<br />
x<br />
i
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