# A Tensor SVD-based Classification Algorithm Applied to fMRI Data

arXiv: https://arxiv.org/abs/2111.00587 · HTML: https://mlsanity.com/paper/2111.00587/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 27 references that are in the map.
- First posted on arXiv 31 Oct 2021.

## Builds on (most cited first, 3 of 3)

- [Jpeg Image Compression Using Discrete Cosine Transform - A Survey](https://mlsanity.com/paper/1405.6147/) (2014)
- [Image classification using local tensor singular value decompositions](https://mlsanity.com/paper/1706.09693/) (2017)
- [Dynamic Graph Convolutional Networks Using the Tensor M-Product](https://mlsanity.com/paper/1910.07643/) (2019)

## Built on by (most cited first, 5 of 5)

- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Optimal Matrix-Mimetic Tensor Algebras via Variable Projection](https://mlsanity.com/paper/2406.06942/) (2024)
- [A Mesh Is Worth 512 Numbers: Spectral-domain Diffusion Modeling for High-dimension Shape Generation](https://mlsanity.com/paper/2503.06485/) (2025)
- [Projected Tensor-Tensor Products for Efficient Computation of Optimal Multiway Data Representations](https://mlsanity.com/paper/2409.19402/) (2024)
- [sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation](https://mlsanity.com/paper/2506.08670/) (2025)

## Abstract (arXiv)

To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the vectorized data. While the SVD is highly useful for data that can be appropriately represented as a matrix, this step of vectorization causes us to lose the high-dimensional relationships intrinsic to the data. To facilitate efficient multidimensional feature extraction, we utilize a projection-based classification algorithm using the t-SVDM, a tensor analog of the matrix SVD. Our work extends the t-SVDM framework and the classification algorithm, both initially proposed for tensors of order 3, to any number of dimensions. We then apply this algorithm to a classification task using the StarPlus fMRI dataset. Our numerical experiments demonstrate that there exists a superior tensor-based approach to fMRI classification than the best possible equivalent matrix-based approach. Our results illustrate the advantages of our chosen tensor framework, provide insight into beneficial choices of parameters, and could be further developed for classification of more complex imaging data. We provide our Python implementation at https://github.com/elizabethnewman/tensor-fmri.