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摘要翻译：
本文提出了一种新的广义多元线性回归模型--高阶偏最小二乘(HOPLS)，其目的是通过将数据投影到潜在空间并对相应的潜在变量进行回归，从张量{X}中预测张量{Y}。HOPLS与其他回归模型的本质不同之处在于，它用一个正交Tucker张量的总和来解释数据，而正交加载数作为控制模型复杂性和防止过拟合的参数。通过压缩操作，对低维潜空间进行优化，得到了对$\tensor{X}$和$\tensor{Y}$的最佳联合子空间逼近。在新定义的广义互协方差张量上，采用高阶奇异值分解来优化正交载荷，而不是单独分解$张量{X}和$张量{Y}。通过对合成数据和基于ECoG信号的三维运动轨迹解码的系统比较，证明了HOPLS比现有方法具有更好的预测能力、适合处理小样本和对噪声的鲁棒性等优点。
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英文标题：
《Higher-Order Partial Least Squares (HOPLS): A Generalized Multi-Linear
Regression Method》
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作者：
Qibin Zhao, Cesar F. Caiafa, Danilo P. Mandic, Zenas C. Chao, Yasuo
Nagasaka, Naotaka Fujii, Liqing Zhang and Andrzej Cichocki
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最新提交年份：
2012
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
A new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) $\tensor{Y}$ from a tensor $\tensor{X}$ through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both $\tensor{X}$ and $\tensor{Y}$. Instead of decomposing $\tensor{X}$ and $\tensor{Y}$ individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.
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PDF链接：
https://arxiv.org/pdf/1207.1230
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