Supervised tensor decomposition with features on multiple modes

Abstract

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of node features and interactions thereof, together with the tensor data. Such data problems are common in neuroimaging, network analysis, and spatial-temporal modeling. Identifying the relationship between a high-dimensional tensor and side information is important yet challenging. Here, we develop a tensor decomposition method that incorporates multiple feature matrices as side information. Unlike unsupervised tensor decomposition, our supervised decomposition captures the effective dimension reduction of the data tensor confined to feature space of interest. An efficient alternating optimization algorithm with provable spectral initialization is further developed. Our proposal handles a broad range of data types, including continuous, count, and binary observations. We apply the method to diffusion tensor imaging data from human connectome project and multi-relational political network data. We identify the key global connectivity pattern and pinpoint the local regions that are associated with available features. Our simulation code, R-package tensorregress, and datasets used in the paper are available at https://CRAN.R-project.org/package=tensorregress.

arXiv comment51 pages, 9 figures

References in corpus (11)

• Joint and individual variation explained (JIVE) for integrated analysis of multiple data types
• Tensor Regression with Applications in Neuroimaging Data Analysis
• On Tensors, Sparsity, and Nonnegative Factorizations
• Generalized Canonical Polyadic Tensor Decomposition
• Inference and Uncertainty Quantification for Noisy Matrix Completion
• Tensor-on-tensor regression
• A novel approach for fusion of heterogeneous sources of data
• Supervised multiway factorization
• Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence
• Regularized and Smooth Double Core Tensor Factorization for Heterogeneous Data
• Beyond the Signs: Nonparametric Tensor Completion via Sign Series

Cited by in corpus (2)

• Semi-parametric TEnsor Factor Analysis by Iteratively Projected Singular Value Decomposition
• Multiway Spherical Clustering via Degree-Corrected Tensor Block Models