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. The package and data used are available at https://CRAN.R-project.org/package=tensorregress. Supplementary materials for this article are available online.
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Learning Multiple Networks via Supervised Tensor Decomposition
We consider the problem of tensor decomposition with multiple side information available as interactive features. Such problems are common in neuroimaging, network modeling, and spatial-temporal analysis. We develop a new family of exponential tensor decomposition models and establish the theoretical accuracy guarantees. An efficient alternating optimization algorithm is further developed. Unlike earlier methods, our proposal is able to handle 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 identify the key brain connectivity patterns associated with available features. Our method will help the practitioners efficiently analyze tensor datasets in various areas. Toward this end, all data and code are available at https://CRAN.R-project.org/ package=tensorregress.
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- Award ID(s):
- 1915978
- NSF-PAR ID:
- 10345832
- Date Published:
- Journal Name:
- Third Workshop on Machine Learning and the Physical Sciences (NeurIPS 2020), Vancouver, Canada.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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