When data are organized in matrices or arrays of higher dimensions (tensors), classical regression methods first transform these data into vectors, therefore ignoring the underlying structure of the data and increasing the dimensionality of the problem. This flattening operation typically leads to overfitting when only few training data is available. In this paper, we present a mixture-of-experts model that exploits tensorial representations for regression of tensor-valued data. The proposed formulation takes into account the underlying structure of the data and remains efficient when few training data are available. Evaluation on artificially generated data, as well as offline and real-time experiments recognizing hand movements from tactile myography prove the effectiveness of the proposed approach.

当数据以较高维度（张量）的矩阵或阵列进行组织时，经典的回归方法首先将这些数据转换为向量，因此忽略了数据的底层结构并增加了问题的维度。当只有很少的训练数据可用时，这种扁平化操作通常会导致过度拟合。在本文中，我们提出了一种专家混合模型，该模型利用张量表示法对张量值数据进行回归。所提出的公式考虑到了数据的基本结构，并且在几乎没有可用的训练数据时仍然有效。对人工生成的数据进行的评估以及脱机和实时实验可以识别来自触觉肌腱的手部运动，从而证明了该方法的有效性。