Convex collective matrix factorization

A method operative on observed relationship data between pairs of entities of a set of entities, the set of entities including entities of at least two different entity types, the method comprising:

• constructing an observed collective symmetric matrix in which element (n,m) equals element (m,n) and stores the observed relationship between entities of the set of entities indexed n and m conditional upon the observed relationship data including an observed relationship between the entities indexed n and m;
• optimizing a prediction collective symmetric matrix in order to minimize a loss function comparing the observed collective symmetric matrix and the prediction collective symmetric matrix, the optimizing generating an optimized prediction collective symmetric matrix;
• and
• predicting a relationship between two entities of the set of entities using the optimized prediction collective symmetric matrix;
• wherein the constructing, the optimizing, and the predicting are performed by an electronic data processing device.

An apparatus operative on observed relationship data between pairs of entities of a set of entities, the set of entities including entities of at least two different entity types, the apparatus comprising:

• an electronic data processing device programmed to perform operations including:
• constructing an observed collective symmetric matrix Y in which element (n,m) equals element (m,n) and stores the observed relationship between entities of the set of entities indexed n and m conditional upon the observed relationship data including an observed relationship between the entities indexed n and m;
• and
• optimizing a prediction collective symmetric matrix X in order to minimize a convex loss function l(X,Y)+λ∥X∥* where l(X,Y) is a function comparing the prediction collective symmetric matrix X and the observed collective symmetric matrix Y, λ∥X∥* is the trace norm of the prediction collective symmetric matrix X, and λ is a scalar value.