Tensor decomposition with generalized lasso penalties

TL;DR

This paper introduces a penalized tensor decomposition method with generalized lasso penalties that effectively captures smoothly varying latent factors in multi-way data, improving analysis of spatial and temporal features.

Contribution

The paper develops a novel penalized tensor decomposition framework with an efficient optimization algorithm, extending sparse tensor and matrix decompositions to incorporate smoothness penalties.

Findings

Improved analysis of multi-way data with spatial or temporal smoothness.

Efficient coordinate-wise optimization algorithm with proven convergence.

Successful application to simulated and real flu hospitalization data.

Abstract

We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multi-way data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our approach presents many nontrivial challenges at the intersection of modeling and computation, which are studied in detail. An efficient coordinate-wise optimization algorithm for (PTD) is presented, and its convergence properties are characterized. The method is applied both to simulated data and real data on flu hospitalizations in Texas. These results show that our penalized tensor decomposition can offer major improvements on existing methods for analyzing multi-way data that exhibit smooth spatial or temporal features.