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Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification

机译:高阶张量数据分类的多线性判别分析

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In the past decade, great efforts have been made to extend linear discriminant analysis for higher-order data classification, generally referred to as multilinear discriminant analysis (MDA). Existing examples include general tensor discriminant analysis (GTDA) and discriminant analysis with tensor representation (DATER). Both the two methods attempt to resolve the problem of tensor mode dependency by iterative approximation. GTDA is known to be the first MDA method that converges over iterations. However, its performance relies highly on the tuning of the parameter in the scatter difference criterion. Although DATER usually results in better classification performance, it does not converge, yet the number of iterations executed has a direct impact on DATER’s performance. In this paper, we propose a closed-form solution to the scatter difference objective in GTDA, namely, direct GTDA (DGTDA) which also gets rid of parameter tuning. We demonstrate that DGTDA outperforms GTDA in terms of both efficiency and accuracy. In addition, we propose constrained multilinear discriminant analysis (CMDA) that learns the optimal tensor subspace by iteratively maximizing the scatter ratio criterion. We prove both theoretically and experimentally that the value of the scatter ratio criterion in CMDA approaches its extreme value, if it exists, with bounded error, leading to superior and more stable performance in comparison to DATER.
机译:在过去的十年中,人们为将线性判别分析扩展到高阶数据分类做出了巨大的努力,通常被称为多线性判别分析(MDA)。现有的示例包括一般张量判别分析(GTDA)和带张量表示的判别分析(DATER)。两种方法都试图通过迭代逼近来解决张量模式依赖性问题。众所周知,GTDA是第一种通过迭代收敛的MDA方法。但是,其性能高度依赖于散射差异准则中参数的调整。尽管DATER通常可以带来更好的分类性能,但它不会收敛,但是执行的迭代次数会直接影响DATER的性能。本文针对GTDA中的散射差异目标提出了一种封闭形式的解决方案,即直接GTDA(DGTDA),它也摆脱了参数调整的麻烦。我们证明DGTDA在效率和准确性方面都优于GTDA。此外,我们提出了一种约束多线性判别分析(CMDA),该方法通过迭代最大化散布比标准来学习最佳张量子空间。我们在理论上和实验上都证明,CMDA中散布比率标准的值接近其极值(如果存在),并且有一定的误差,与DATER相比,它具有更好且更稳定的性能。

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