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1. Generalized Tensor Decomposition With Features on Multiple Modes

   https://doi.org/10.1080/10618600.2021.1978471  

   Hu, Jiaxin; Lee, Chanwoo; Wang, Miaoyan (September 2021, Journal of computational and graphical statistics)

   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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2. Learning Multiple Networks via Supervised Tensor Decomposition

   Hu, Jiaxin; Lee, Chanwoo; Wang, Miaoyan (December 2020, Third Workshop on Machine Learning and the Physical Sciences (NeurIPS 2020), Vancouver, Canada.)

   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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3. Exploring the feasibility of tensor decomposition for analysis of fNIRS signals: a comparative study with grand averaging method

   https://doi.org/10.3389/fnins.2023.1180293  

   Chan, Jasmine Y.; Hssayeni, Murtadha D.; Wilcox, Teresa; Ghoraani, Behnaz (August 2023, Frontiers in Neuroscience)

   The analysis of functional near-infrared spectroscopy (fNIRS) signals has not kept pace with the increased use of fNIRS in the behavioral and brain sciences. The popular grand averaging method collapses the oxygenated hemoglobin data within a predefined time of interest window and across multiple channels within a region of interest, potentially leading to a loss of important temporal and spatial information. On the other hand, the tensor decomposition method can reveal patterns in the data without making prior assumptions of the hemodynamic response and without losing temporal and spatial information. The aim of the current study was to examine whether the tensor decomposition method could identify significant effects and novel patterns compared to the commonly used grand averaging method for fNIRS signal analysis. We used two infant fNIRS datasets and applied tensor decomposition (i.e., canonical polyadic and Tucker decompositions) to analyze the significant differences in the hemodynamic response patterns across conditions. The codes are publicly available on GitHub. Bayesian analyses were performed to understand interaction effects. The results from the tensor decomposition method replicated the findings from the grand averaging method and uncovered additional patterns not detected by the grand averaging method. Our findings demonstrate that tensor decomposition is a feasible alternative method for analyzing fNIRS signals, offering a more comprehensive understanding of the data and its underlying patterns. 

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4. Coupled CP Tensor Decomposition with Shared and Distinct Components for Multi-Task Fmri Data Fusion

   https://doi.org/10.1109/ICASSP49357.2023.10096241  

   Borsoi, R A; Lehmann, I; Akhonda, M_A_B S; Calhoun, V D; Usevich, K; Brie, D; Adali, T (June 2023, IEEE)

   iscovering components that are shared in multiple datasets, next to dataset-specific features, has great potential for studying the relationships between different subjects or tasks in functional Magnetic Resonance Imaging (fMRI) data. Coupled matrix and tensor factorization approaches have been useful for flexible data fusion, or decomposition to extract features that can be used in multiple ways. However, existing methods do not directly recover shared and dataset-specific components, which requires post-processing steps involving additional hyperparameter selection. In this paper, we propose a tensor-based framework for multi-task fMRI data fusion, using a partially constrained canonical polyadic (CP) decomposition model. Differently from previous approaches, the proposed method directly recovers shared and dataset-specific components, leading to results that are directly interpretable. A strategy to select a highly reproducible solution to the decomposition is also proposed. We evaluate the proposed methodology on real fMRI data of three tasks, and show that the proposed method finds meaningful components that clearly identify group differences between patients with schizophrenia and healthy controls. 

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5. Parallel Nonnegative CP Decomposition of Dense Tensors

   https://doi.org/10.1109/HiPC.2018.00012  

   Ballard, Grey; Hayashi, Koby; Ramakrishnan, Kannan (December 2018, 25th IEEE International Conference on High Performance Computing)

   The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensors that can enforce nonnegativity of the computed low-rank factors. The principal task is to parallelize the Matricized-Tensor Times Khatri-Rao Product (MTTKRP) bottleneck subcomputation. The algorithm is computation efficient, using dimension trees to avoid redundant computation across MTTKRPs within the alternating method. Our approach is also communication efficient, using a data distribution and parallel algorithm across a multidimensional processor grid that can be tuned to minimize communication. We benchmark our software on synthetic as well as hyperspectral image and neuroscience dynamic functional connectivity data, demonstrating that our algorithm scales well to 100s of nodes (up to 4096 cores) and is faster and more general than the currently available parallel software. 

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