Quadratic Multilinear Discriminant Analysis for Tensorial Data Classification

Over the past decades, there has been an increase of attention to adapting machine learning methods fully exploit higher order structure tensorial data. One problem great interest is tensor classification, and in particular extension linear discriminant analysis multilinear setting. We propose a novel method for that radically different from ones considered so far, it first tensors quadratic analysis. Our proposed approach uses invariant theory extend nearest Mahalanobis distance classifier higher-order setting, formulate well-behaved optimization problem. extensively test our on variety synthetic data, outperforming previously MDA techniques. also show how leverage multi-lead ECG data by constructing via taut string, use classify healthy signals versus unhealthy ones; outperforms state-of-the-art methods, especially after adding significant levels noise signals. reached AUC 0.95(0.03) clean signals—where second best 0.91(0.03)—and 0.89(0.03) (with signal-to-noise-ratio −30)—where 0.85(0.05). fundamentally than previous work this direction, proves be faster, more stable, accurate tests we performed.