Patent ID: 8498949

Claim:
A method of factorizing a data matrix U file by supervised nonnegative factorization, SNMF, comprising: providing a data processing device to implement the following step: accessing said data matrix U from a data store, wherein data matrix U is defined as U εR d×n ; defining an intrinsic graph G, wherein G={U,W}, each column of U εR d×n represents a vertex, and each element of similarity matrix W measures the similarity between vertex pairs; defining a penalty graph G , wherein G ={U, W } and each element of dissimilarity matrix W measures unfavorable relationships between said vertex pairs; defining an intrinsic diagonal matrix D , wherein D=[D ij ]and D ii =Σ j=1 n W ij ; defining an intrinsic Laplacian matrix L, wherein L =D −W; defining a penalty diagonal matrix D , wherein D =[ D ij ] and D ii =Σ j=1 n W ij ; defining a penalty Laplacian matrix L , wherein L = D − W ; defining a basis matrix V, where V εR dxr ; defining a feature matrix X, where X εR rxn ; defining a measure of the compactness of intrinsic graph G by the weighted sum of squared distances defined as Σ i<j n W ij ∥x i −x j ∥ 2 =Tr(XLX T ), wherein x i is the i-th column of X and x J is j-th column of X; defining a measure of the separability of penalty graph G by the weighted sum of squared distances defined as Σ i<j n W ij ∥x i −x j ∥ 2 =Tr(X L X T ) , wherein x i is the i-th column of X and x j is j-th column of X ; defining F( 1 )(V,X) as an objective of NMF (nonnegative matrix factorization), wherein F( 1 )(V,X)=∥U −VX ∥ F 2 ; defining F( 2 )(X) as an objective of graph embedding, where F ( 2 ) ⁡ ( X ) = Tr ⁡ ( XLX T ) Tr ⁡ ( X ⁢ L _ ⁢ X T ) ; applying Pareto optimality to F( 1 )(V,X) and F( 2 )(X); and defining the final state V*, X* of matrices V and X at the Pareto optimal resulting from application of said Pareto optimality as a factorization of data matrix U.