CONVEX COLLECTIVE MATRIX FACTORIZATION

摘要

A method operates on observed relationship data between pairs of entities of a set of entities including entities of at least two (and optionally at least three) different entity types. An observed collective symmetric matrix is constructed in which element (n,m)=element (m,n) stores the observed relationship between entities indexed n and m when the observed relationship data includes this observed relationship. A prediction collective symmetric matrix is optimized in order to minimize a loss function comparing the observed collective symmetric matrix and the prediction collective symmetric matrix. A relationship between two entities of the set of entities is predicted using the optimized prediction collective symmetric matrix. Entities of the same entity type may be indexed using a contiguous set of indices such that the entity type maps to a contiguous set of rows and corresponding contiguous set of columns in the observed collective symmetric matrix.

主权项

1. A non-transitory storage medium storing instructions executable by an electronic data processing device to perform a method including:
constructing an observed collective symmetric matrix Y storing observed relationship data between pairs of entities for E entities of K different entity types where K is greater than or equal to two with nk entities belonging to entity type k for k=1, . . . , K and E=nl+ . . . +nK, the observed collective symmetric matrix Y being a symmetric matrix with E rows for the E entities and E columns for the E entities, optimizing a prediction collective symmetric matrix X that is also a symmetric matrix with E rows for the E entities and E columns for the E entities in order to minimize a loss function comparing the observed collective symmetric matrix Y with the prediction collective symmetric matrix X, the optimizing generating an optimized prediction collective symmetric matrix Xopt, and performing a prediction operation for a first entity of the E entities given a second entity of the E entities based on an element of the optimized prediction collective symmetric matrix Xopt corresponding to the first and second entities.