Kernelized Support Tensor Machines

Lifang He, Chun-Ta Lu, Guixiang Ma, Shen Wang, Linlin Shen, Philip S. Yu, Ann B. Ragin
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1442-1451, 2017.

Abstract

In the context of supervised tensor learning, preserving the structural information and exploiting the discriminative nonlinear relationships of tensor data are crucial for improving the performance of learning tasks. Based on tensor factorization theory and kernel methods, we propose a novel Kernelized Support Tensor Machine (KSTM) which integrates kernelized tensor factorization with maximum-margin criterion. Specifically, the kernelized factorization technique is introduced to approximate the tensor data in kernel space such that the complex nonlinear relationships within tensor data can be explored. Further, dual structural preserving kernels are devised to learn the nonlinear boundary between tensor data. As a result of joint optimization, the kernels obtained in KSTM exhibit better generalization power to discriminative analysis. The experimental results on real-world neuroimaging datasets show the superiority of KSTM over the state-of-the-art techniques.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-he17a, title = {Kernelized Support Tensor Machines}, author = {Lifang He and Chun-Ta Lu and Guixiang Ma and Shen Wang and Linlin Shen and Philip S. Yu and Ann B. Ragin}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {1442--1451}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/he17a/he17a.pdf}, url = {https://proceedings.mlr.press/v70/he17a.html}, abstract = {In the context of supervised tensor learning, preserving the structural information and exploiting the discriminative nonlinear relationships of tensor data are crucial for improving the performance of learning tasks. Based on tensor factorization theory and kernel methods, we propose a novel Kernelized Support Tensor Machine (KSTM) which integrates kernelized tensor factorization with maximum-margin criterion. Specifically, the kernelized factorization technique is introduced to approximate the tensor data in kernel space such that the complex nonlinear relationships within tensor data can be explored. Further, dual structural preserving kernels are devised to learn the nonlinear boundary between tensor data. As a result of joint optimization, the kernels obtained in KSTM exhibit better generalization power to discriminative analysis. The experimental results on real-world neuroimaging datasets show the superiority of KSTM over the state-of-the-art techniques.} }
Endnote
%0 Conference Paper %T Kernelized Support Tensor Machines %A Lifang He %A Chun-Ta Lu %A Guixiang Ma %A Shen Wang %A Linlin Shen %A Philip S. Yu %A Ann B. Ragin %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-he17a %I PMLR %P 1442--1451 %U https://proceedings.mlr.press/v70/he17a.html %V 70 %X In the context of supervised tensor learning, preserving the structural information and exploiting the discriminative nonlinear relationships of tensor data are crucial for improving the performance of learning tasks. Based on tensor factorization theory and kernel methods, we propose a novel Kernelized Support Tensor Machine (KSTM) which integrates kernelized tensor factorization with maximum-margin criterion. Specifically, the kernelized factorization technique is introduced to approximate the tensor data in kernel space such that the complex nonlinear relationships within tensor data can be explored. Further, dual structural preserving kernels are devised to learn the nonlinear boundary between tensor data. As a result of joint optimization, the kernels obtained in KSTM exhibit better generalization power to discriminative analysis. The experimental results on real-world neuroimaging datasets show the superiority of KSTM over the state-of-the-art techniques.
APA
He, L., Lu, C., Ma, G., Wang, S., Shen, L., Yu, P.S. & Ragin, A.B.. (2017). Kernelized Support Tensor Machines. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:1442-1451 Available from https://proceedings.mlr.press/v70/he17a.html.

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