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We eliminate the
noise model for each data component,
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and we use the same
number of factors as data
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components.
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Given the weight
matrix, there is now a one-to-one
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mapping between
data vectors and hidden activity
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vectors.
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To make the data
probable we want two things:
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The
hidden activity vectors that correspond to data
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vectors
should have high prior probabilities.
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The
mapping from hidden activities to data vectors
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should
compress the hidden density to get high density
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in
the data space. i.e. the matrix that maps hidden
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activities
to data vectors should have a small
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determinant.
Its inverse should have a big determinant
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