Abstract

Modern data often take the form of a multiway array. However, most classification methods are designed for vectors, that is, one-way arrays. Distance weighted discrimination (DWD) is a popular high-dimensional classification method that has been extended to the multiway context, with dramatic improvements in performance when data have multiway structure. However, the previous implementation of multiway DWD was restricted to classification of matrices, and did not account for sparsity. In this article, we develop a general framework for multiway classification which is applicable to any number of dimensions and any degree of sparsity. We conducted extensive simulation studies, showing that our model is robust to the degree of sparsity and improves classification accuracy when the data have multiway structure. For our motivating application, magnetic resonance spectroscopy (MRS) was used to measure the abundance of several metabolites across multiple neurological regions and across multiple time points in a mouse model of Friedreich’s ataxia, yielding a four-way data array. Our method reveals a robust and interpretable multi-region metabolomic signal that discriminates the groups of interest. We also successfully apply our method to gene expression time course data for multiple sclerosis treatment. An R implementation is available in the package MultiwayClassification at http://github.com/lockEF/MultiwayClassification. Supplementary materials for this article are available online.

 抽象的

现代数据通常采用多路数组的形式。然而，大多数分类方法都是针对向量（即单向数组）设计的。距离加权判别（DWD）是一种流行的高维分类方法，已扩展到多路环境，当数据具有多路结构时，性能显着提高。然而，之前多路DWD的实现仅限于矩阵分类，并没有考虑稀疏性。在本文中，我们开发了一个多路分类的通用框架，该框架适用于任何数量的维度和任何稀疏程度。我们进行了广泛的模拟研究，表明我们的模型在稀疏程度方面具有鲁棒性，并且当数据具有多路结构时可以提高分类准确性。对于我们的激励应用，磁共振波谱 (MRS) 用于测量弗里德赖希共济失调小鼠模型中多个神经区域和多个时间点的几种代谢物的丰度，产生四路数据阵列。我们的方法揭示了一个强大且可解释的多区域代谢组信号，可以区分感兴趣的群体。我们还成功地将我们的方法应用于多发性硬化症治疗的基因表达时程数据。 R 实现可在 http://github.com/lockEF/MultiwayClassification 的MultiwayClassification包中找到。本文的补充材料可在线获取。