ABSTRACT Sufficient dimension reduction (SDR) techniques have proven to be very useful data analysis tools in various applications. Conventional SDR methods mainly tackle simple vector-valued predictors, but they are inappropriate for data with array (tensor)-valued predictors. In this paper, we propose a tensor dimension reduction approach based on inverse regression, and we refer to it as T-IRE, which reduces the dimension of original array-valued predictors while simultaneously retaining the structural information within predictors and the proposed method also provides an efficient estimation algorithm. Empirical performance and two dataset analysis demonstrate the advantages of our proposed method.

中文翻译：

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通过张量逆回归进行足够的维度折叠

摘要 充分降维 (SDR) 技术已被证明是各种应用中非常有用的数据分析工具。传统的 SDR 方法主要处理简单的向量值预测变量，但它们不适用于具有数组（张量）值预测变量的数据。在本文中，我们提出了一种基于逆回归的张量降维方法，我们将其称为 T-IRE，它降低了原始数组值预测器的维数，同时保留了预测器内的结构信息，并且该方法还提供了一种有效的估计算法。经验表现和两个数据集分析证明了我们提出的方法的优势。