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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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A Supervised Tensor Dimension Reduction-Based Prognostic Model for Applications with Incomplete Imaging Data
Imaging data-based prognostic models focus on using an asset’s degradation images to predict its time to failure (TTF). Most image-based prognostic models have two common limitations. First, they require degradation images to be complete (i.e., images are observed continuously and regularly over time). Second, they usually employ an unsupervised dimension reduction method to extract low-dimensional features and then use the features for TTF prediction. Because unsupervised dimension reduction is conducted on the degradation images without the involvement of TTFs, there is no guarantee that the extracted features are effective for failure time prediction. To address these challenges, this article develops a supervised tensor dimension reduction-based prognostic model. The model first proposes a supervised dimension reduction method for tensor data. It uses historical TTFs to guide the detection of a tensor subspace to extract low-dimensional features from high-dimensional incomplete degradation imaging data. Next, the extracted features are used to construct a prognostic model based on (log)-location-scale regression. An optimization algorithm for parameter estimation is proposed, and analytical solutions are discussed. Simulated data and a real-world data set are used to validate the performance of the proposed model. History: Bianca Maria Colosimo served as the senior editor for this article Funding: This work was supported by National Science Foundation [2229245]. Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://github.com/czhou9/Code-and-Data-for-IJDS and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2022.x022 ).
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- Award ID(s):
- 2229245
- PAR ID:
- 10545690
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- INFORMS Journal on Data Science
- Volume:
- 3
- Issue:
- 1
- ISSN:
- 2694-4022
- Page Range / eLocation ID:
- 84 to 104
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/ijds.2022.x022
