High-Order Multilinear Discriminant Analysis via Order-$\textit{n}$ Tensor Eigendecomposition
This work addresses classification challenges for researchers and practitioners in machine learning and computer vision dealing with high-dimensional tensor data, though it appears incremental as it builds upon existing multilinear discriminant analysis frameworks.
The paper tackles the problem of classifying higher-order data by proposing a new tensor-based multilinear discriminant analysis method, HOMLDA, and its robust variant RHOMLDA, which show improved classification performance over existing Tucker decomposition-based methods on multiple datasets.
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 $\textit{n}$-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-$\textit{n}$ tensor can be written as a product of order-$\textit{n}$ 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.