Matrix Factorization with Side and Higher Order Information.

The problem of predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees have been developed for algorithms where the matrix is factored into low-rank components, and embeddings are learned for the row and column variables. While there has been recent research on incorporating explicit side information in the low-rank matrix factorization setting, often implicit information can be gleaned from the data, via higher order interactions among variables. In this paper, we design a method to make use of this implicit information, via random walks on graphs. We show that the problem we intend to solve can be cast as factoring a nonlinear transform of the (partially) observed matrix and develop an efficient coordinate descent based algorithm for the same. Experiments on several datasets show that the method we propose outperforms vanilla matrix factorization, and also those methods that use explicitly available side information.