Spectral Embedded Clustering
نویسندگان
چکیده
∀i, yi = [0, ..., 0 } {{ } j−1 , 1, 0, ..., 0 } {{ } c−j ] ⇒ xi W0 = x̄j W0, (1) where y i is the i-th row of the true cluster assignment matrix Y and x̄j is the mean of the data that belongs to class j. Denote X̄c = [x̄1, ..., x̄c]. Note that X̄c = XY Σ, where Σ ∈ Rc×c is a diagonal matrix with the i-th diagonal element as 1/ni, ni is the number of the data that belongs to class i. Then rank(X̄ c W0) = rank(ΣY T X (XX )XY ) = rank((XX )XY ) = rank(Sb) = c− 1. Denote
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