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We need a
sensible measure of what it means to cluster
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the data well.
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This
makes it possible to judge different methods.
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It
may make it possible to decide on the number of
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clusters.
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An obvious
approach is to imagine that the data was
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produced by a
generative model.
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Then
we can adjust the parameters of the model to
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maximize
the probability density that it would produce
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exactly
the data we observed.
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