Novel Fast Linear Discriminant Analysis (F-TLDA) for Arbitrary-Dimensional Tensor Signal Data

Document Type

Article

Publication Date

1-1-2026

Abstract

Linear discriminant analysis (LDA) has been widely adopted for dimensionality reduction in pattern recognition and classification in data engineering for long. However, it is still quite challenging when one applies the existing LDA to deal with arbitrary-dimensional tensor signal data, especially, computationally-efficiently. To tackle this problem, we recently proposed the tensor linear discriminant analysis (a.k.a. TLDA), which was based on the Einstein (tensor) product. Unfortunately, TLDA is often incurred with high computational-complexity and hence it would encounter the scalability problem (i.e., it cannot be easily extended to data tensors with high dimensions). In this work, we would like to introduce a novel fast tensor linear discriminant analysis (F-TLDA) for arbitrary-dimensional signal data. For doing so, we establish a tensor Courant- Fischer theorem, derive a preconditioned conjugate gradient (PCG) rule for solving linear tensor equations, and develop a parallel generalized tensor power-iteration PCG (P-GTPI-PCG) scheme to determine the feature subspace composed by the k dominant eigenvalues and the corresponding eigentensors at the cost of a quadratic computational-complexity with respect to the product of all tensor dimensions. Furthermore, we also study the convergence behavior of our proposed P-GTPI-PCG method with respect to the eigen-spread and various preconditioners. Numerical experiments have been carried out to evaluate the computational-complexities and the classification accuracies of our proposed new P-GTPI-PCG method in comparison with four major existing schemes. Meanwhile, such experiments have also been utilized to demonstrate the outstanding (fast) convergence speeds of our proposed new P-GTPI-PCG method. The corresponding results show that our proposed P-GTPI-PCG method greatly outperforms other existing schemes in comparison in terms of computational-complexity and classification accuracy.

Publication Title

IEEE Transactions on Knowledge and Data Engineering

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