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Suppose each
data point is N-dimensional
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Same procedure
applies:
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The eigenvectors
of A define a new coordinate system
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eigenvector with
largest eigenvalue captures the most variation among
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training vectors x
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eigenvector with
smallest eigenvalue has least variation
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We can compress
the data by only using the top few eigenvectors
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corresponds to
choosing a “linear subspace”
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represent points
on a line, plane, or “hyper-plane”
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these
eigenvectors are known as the principal components
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