Learning Tensor Latent Features

Compared to the classic latent factor models [14], latent feature models have two main benefits: (1) interpretablity: the binary codes directly reveal whether certain features exist in the data, thus provide more interpretable latent profiles [25]; (2) scalability: compared with real-valued codes, binary codes require fewer bits to store, thereby cutting down the memory footprint, making it easier to deploy into memory constrained environments such as mobile devices. Tensor latent feature models generalize traditional matrix latent feature models to represent high-order correlation structures in the data. For example, in spatiotemporal recommender systems, the observations are user activities over different locations and time. We want to learn the latent features and codes that correspond to user, space and time simultaneously without assuming conditional independence of these three dimensions. In this case, we can first represent such data as a high-order tensor and assign binary codes encoding presence or absence of rows for individual modes of the tensor. These codes can then help us answer the "when" and "where" questions regarding the learned user preferences. Besides the non-convex formulation of the maximum likelihood estimation (MLE) objective, learning latent feature models is further complicated by the combinatorial nature of the codes.