Scalable Tensor Factorizations for Incomplete Data

Details Scalable Tensor Factorizations for Incomplete Data Scalable Tensor Factorizations for Incomplete Data

2010-05-12

arxiv.org/abs/1005.2197v1

Chemometrics and Intelligent Laboratory Systems 106(1):41-56, Mar. 2011

Mathematics

Numerical Analysis

Scientific paper

10.1016/j.chemolab.2010.08.004

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 and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 x 1000 x 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP-WOPT on two real-world 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.

Affiliated with

Also associated with

No associations

Rating

Scalable Tensor Factorizations for Incomplete Data does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Scalable Tensor Factorizations for Incomplete Data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scalable Tensor Factorizations for Incomplete Data will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-639855