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Higher Order Partial Least Squares (HOPLS): A Generalized Multilinear Regression Method
July 2013 (vol. 35 no. 7)
pp. 1660-1673
Qibin Zhao, Lab. for Adv. Brain Signal Process., RIKEN, Saitama, Japan
C. F. Caiafa, Inst. Argentino de Radioastronom. (IAR), CCT La Plata, Buenos Aires, Argentina
D. P. Mandic, Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK
Z. C. Chao, Lab. for Adaptive Intell., RIKEN, Saitama, Japan
Y. Nagasaka, Lab. for Adaptive Intell., RIKEN, Saitama, Japan
N. Fujii, Lab. for Adaptive Intell., RIKEN, Saitama, Japan
Liqing Zhang, Dept. of Comput. Sci. & Eng., Shanghai Jiao Tong Univ., Shanghai, China
A. Cichocki, Lab. for Adv. Brain Signal Process., RIKEN, Saitama, Japan
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) Y from a 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 X and Y. Instead of decomposing X and 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 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.
Index Terms:
Tensile stress,Vectors,Approximation methods,Matrix decomposition,Loading,Optimization,Data models,fusion of behavioral and neural data,Multilinear regression,partial least squares,higher order singular value decomposition,constrained block Tucker decomposition,electrocorticogram
Citation:
Qibin Zhao, C. F. Caiafa, D. P. Mandic, Z. C. Chao, Y. Nagasaka, N. Fujii, Liqing Zhang, A. Cichocki, "Higher Order Partial Least Squares (HOPLS): A Generalized Multilinear Regression Method," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 7, pp. 1660-1673, July 2013, doi:10.1109/TPAMI.2012.254
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