Scalable Tensor Factorizations for Incomplete Data  Evrim Acar, Daniel M. Dunlavy, Tamara G. Kolda, Morten Mørup
 Abstract  The problem of incomplete data—i.e., data with missing or unknown values—in multiway 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 wellknown tensor factorizations that captures multilinear 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 CPWOPT (CP Weighted OPTimization) that uses a firstorder optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse largescale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CPWOPT on two realworld applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process.  Keywords  missing data; incomplete data; tensor factorization; CANDECOMP; PARAFAC; optimization  Type  Journal paper [With referee]  Journal  Chemometrics and Intelligent Laboratory Systems  Year  2011 Vol. 106 No. 1 pp. 4156  BibTeX data  [bibtex]  IMM Group(s)  Intelligent Signal Processing 
Back :: IMM Publications
