Collective Tensor Completion with Multiple Heterogeneous Side Information

Huiyuan Chen, Jing Li

Abstract: Tensor completion has been successfully applied to many real-world applications. In a wide variety of situations, data utilized in many learning tasks are of high dimensions, usually extracted from multiple heterogeneous sources. Therefore, data can be represented by a primary tensor and multiple matrices generated from multi-view side information or metadata. Joint analysis of tensors and matrices has great potential to gain better understanding of the underlying relationships among these multiple heterogeneous sources. The existing tensor completion methods, which recover the missing elements of a partially known tensor with single view side information, can yield interpretable results for large-scale datasets. However, their limitations up to now are lack of modeling multi-view heterogeneous data and suitably learning the low-rank property of tensor. In this study, we fill this gap by developing a novel collective tensor completion method, which tightly fuses multi-view heterogeneous data sources. Our method exploits special common latent structures from the primary tensor and multiple side matrices through coupled tensor-matrix decomposition, in which the common latent structures can compactly represent all the data. In addition, rank estimation of a tensor is a challenging task due to its discrete nature. Instead of approximating the rank by widely used trace norm or nuclear norm, we directly utilize Schatten p-norm on the latent structures to better approximate the rank and to enhance its robustness to noise.