CS 598 : Theoretical Machine Learning
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چکیده
In the last lecture, we were looking at clustering sparse graphs in the stochastic block model with parameters p > q, where p = a n , and q = b n , we saw that we could not do perfect clustering as w.h.p, there will be a constant fraction of isolated vertices. However, we shall see that we can still do weak recovery, i.e., by allowing a small fraction of vertices to be misplaced, we will recover the rest of the vertices with relatively good guarantees.
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CS 598 : Theoretical Machine Learning
If this is was what we had from the start then the task of clustering would be trivial. However, usually, the graphs that must be clustered are not this perfect and contain edges between S1 and S2. These edges can be considered noise in the representation of G. Therefore, a clustering algorithm would be attempting to cluster a noisy representation, G ′ , of the perfect graph G. More explicitly,...
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