Scalable Tensor Factorizations for Incomplete Data

The problem of incomplete data--i.e., data with missing or unknown values--in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP). In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) that uses a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factorize tensors with noise ...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Evrim Acar, Tamara G. Kolda, Daniel M. Dunlavy, Morten Mørup
• Keywords: Biomedical Signal Processing, CORR 2010, Education, Missing Values, Network Traffic