# High-Order Multilinear Discriminant Analysis via Order-textitn Tensor Eigendecomposition

arXiv: https://arxiv.org/abs/2205.09191 · HTML: https://mlsanity.com/paper/2205.09191/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 44 references that are in the map.
- First posted on arXiv 18 May 2022.

## Builds on (most cited first, 2 of 2)

- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction](https://mlsanity.com/paper/1506.04954/) (2015)

## Built on by (most cited first, 1 of 1)

- [Multilinear subspace learning for person re-identification based fusion of high order tensor features](https://mlsanity.com/paper/2505.15825/) (2025)

## Abstract (arXiv)

Higher-order data with high dimensionality is of immense importance in many areas of machine learning, computer vision, and video analytics. Multidimensional arrays (commonly referred to as tensors) are used for arranging higher-order data structures while keeping the natural representation of the data samples. In the past decade, great efforts have been made to extend the classic linear discriminant analysis for higher-order data classification generally referred to as multilinear discriminant analysis (MDA). Most of the existing approaches are based on the Tucker decomposition and textitn-mode tensor-matrix products. The current paper presents a new approach to tensor-based multilinear discriminant analysis referred to as High-Order Multilinear Discriminant Analysis (HOMLDA). This approach is based upon the tensor decomposition where an order-textitn tensor can be written as a product of order-textitn tensors and has a natural extension to traditional linear discriminant analysis (LDA). Furthermore, the resulting framework, HOMLDA, might produce a within-class scatter tensor that is close to singular. Thus, computing the inverse inaccurately may distort the discriminant analysis. To address this problem, an improved method referred to as Robust High-Order Multilinear Discriminant Analysis (RHOMLDA) is introduced. Experimental results on multiple data sets illustrate that our proposed approach provides improved classification performance with respect to the current Tucker decomposition-based supervised learning methods.