Patent Document ID: 8499022
Application ID: 13476100

Base Claim:
1. A method of determining a consensus clustering and correspondence matrices from a plurality of membership matrices, comprising: iteratively computing, with an automated processor, from r membership matrices M (1) ∈ n×k1 , . . . , M (r) ∈ n×kr , k∈ + , the consensus clustering represented by M∈ n×k and the r correspondence matrices S (1) ∈ k×k , . . . , S (h) ∈ kh×k , by minimization of an objective function comprising a consensus function f, updating S (h) using update rule: S ( h ) ← S ( h ) - Θ ⊙ ( ∂ f ∂ S ( h ) ) until predetermined convergence conditions are achieved, wherein ⊙ denotes the Hadamard product of two matrices, Θ is a matrix of step size parameters, and updating M using update rule: M ← M = 1 r ⁢ ∑ h = 1 r ⁢ M ( h ) ⁢ S ( h ) until predetermined convergence conditions are achieved; and storing the computed consensus clustering and the correspondence matrices in a memory.

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Claim 6:
6. The method according to claim 1 , wherein Θ = S ( h ) 2 ⁢ D , and D = ( M ( h ) ) T ⁢ M ( h ) ⁢ S ( h ) - α ⁢ ⁢ S ( h ) + α k h ⁢ 1 k h ⁢ k h ⁢ S ( h ) + β ⁢ ⁢ kS ( h ) ⁢ 1 kk , such that the updating rule for S (h) is: S ( h ) ← S ( h ) ⊙ ( M ( h ) ) T ⁢ M + β ⁢ ⁢ k ⁢ ⁢ 1 k h ⁢ k D + ɛ , where: α is a constant ≧0, selected to enforce a column-sparseness constraint, and β is a scaling constant ≧0, for scaling a penalty term added to a consensus function f(M,S (1) ,S (2) , . . . , S (r) ) to deal with an external constraint ∑ j ⁢ S ij ( h ) = 1 efficiently, k denotes the number of clusters, 1 khkh denotes a k h -by-k h matrix of 1s, and ε is a very small positive number used to avoid dividing by 0.