Tensor decomposition with generalized lasso penalties
This work addresses the analysis of multi-way data with smooth spatial or temporal features, representing an incremental advancement by generalizing existing sparse tensor decomposition and penalized matrix methods.
The authors tackled the problem of estimating smoothly varying latent factors in multi-way data by developing a penalized tensor decomposition approach, which showed major improvements over existing methods in applications to simulated and real flu hospitalization data in Texas.
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.