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Suppose that we want to cluster data in
a way that
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guarantees that
we still have a good model even if an
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adversary
removes one of the cluster centers from our
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model.
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E-step: find the
two cluster centers that are closest to
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each data point.
Each of these cluster centers is given a
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responsibility of
0.5 for that datapoint.
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M-step:
Re-estimate each cluster center to be the mean
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of the datapoints
it is responsible for.
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Proof that it
converges:
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The
E-step optimizes F subject to the constraint that
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the
distribution contains 0.5 in two places.
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The
M-step optimizes F with the distribution fixed
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