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This takes
N-dimensional data and finds the M orthogonal
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directions in
which the data has the most variance
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These
M principal directions form a subspace.
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We
can represent an N-dimensional datapoint by its
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projections
onto the M principal directions
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This
loses all information about where the datapoint is located
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in the
remaining orthogonal directions.
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We
reconstruct by using the mean value (over all the
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data)
on the N-M directions that are not represented.
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The
reconstruction error is the sum over all these
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unrepresented
directions of the squared differences from the
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mean.
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