Supervised nonnegative matrix factorization

摘要

Graph embedding is incorporated into nonnegative matrix factorization, NMF, while using the original formulation of graph embedding. Negative values are permitted in the definition of graph embedding without violating the nonnegative requirement of NMF. The factorized matrices of NMF are found by an iterative process.

主权项

1. A pattern recognition method, comprising:
providing a data processing device to implement the following steps: accessing multiple sets of training data, each set of training data having at least one of a true example of a pattern to be recognized or a false example of a pattern to be recognized; arranging said multiple sets of data into a data matrix U in an electronic memory constituting a data store, wherein each set of training data is arranged as a separate column in data matrix U and data matrix U is defined as Uεd×n, where is the set of real numbers and d×n define the dimensions of data matrix U; defining an intrinsic graph G to label specific features of most interest in the sets of training data, wherein G={U,W}, labels that identify favorable features that are features characteristic of the pattern to be recognized are added to the sets of training data in U, each column of U represents a vertex, W is a similarity matrix and each element of similarity matrix W measures the similarity between vertex pairs; defining a penalty graph G to label specific features of least interest in the sets of training data, wherein G={U, W}, labels that identify unfavorable features that are features not characterisic of the pattern to be recognized are added to the sets of training data in U, W is a dissimilarity matrix, and each element of dissimilarity matrix W measures unfavorable relationships between said vertex pairs; defining an intrinsic diagonal matrix D, wherein D=[Dij] and Dii=Σj=1nWij; defining an intrinsic Laplacian matrix L, wherein L=D−W; defining a penalty diagonal matrix D, wherein D=[ Dij] and Dii=Σj=1n= Wij; defining a penalty Laplacian matrix L, wherein L= D− W; defining a basis matrix V, wherein Vεd×r and basis matrix V is to hold basis examples of the sets of training data, the basis examples being a reduction of the sets of training data into simplified representations that highlight distinguishing characteristics of the pattern to be recognized; defining a feature matrix X, wherein Xεr×n feature matrix X is to hold features values to construct an approximation of U from basis matrix V; incorporating the label information of intrinsic graph G and penalty graph G into the construction of basis matrix V and features matrix X by defining a measure of the compactness of intrinsic graph G by the weighted sum of squared distances defined as Σi