TY - GEN

T1 - Least squares support tensor machine

AU - Lv, Meng

AU - Zhao, Xinbin

AU - Song, Lujia

AU - Shi, Haifa

AU - Jing, Ling

PY - 2013

Y1 - 2013

N2 - Least squares support vector machine (LS-SVM), as a variant of the standard support vector machine (SVM) operates directly on patterns represented by vector and obtains an analytical solution directly from solving a set of linear equations instead of quadratic programming (QP). Tensor representation is useful to reduce the overfitting problem in vector-based learning, and tensor-based algorithm requires a smaller set of decision variables as compared to vector-based approaches. Above properties make the tensor learning specially suited for small-sample-size (S3) problems. In this paper, we generalize the vectorbased learning algorithm least squares support vector machine to the tensor-based method least squares support tensor machine (LS-STM), which accepts tensors as input. Similar to LS-SVM, the classifier is obtained also by solving a system of linear equations rather than a QP. LS-STM is based on the tensor space, with tensor representation, the number of parameters estimated by LS-STM is less than the number of parameters estimated by LS-SVM, and avoids discarding a great deal of useful structural information. Experimental results on some benchmark datasets indicate that the performance of LS-STM is competitive in classification performance compared to LS-SVM.

AB - Least squares support vector machine (LS-SVM), as a variant of the standard support vector machine (SVM) operates directly on patterns represented by vector and obtains an analytical solution directly from solving a set of linear equations instead of quadratic programming (QP). Tensor representation is useful to reduce the overfitting problem in vector-based learning, and tensor-based algorithm requires a smaller set of decision variables as compared to vector-based approaches. Above properties make the tensor learning specially suited for small-sample-size (S3) problems. In this paper, we generalize the vectorbased learning algorithm least squares support vector machine to the tensor-based method least squares support tensor machine (LS-STM), which accepts tensors as input. Similar to LS-SVM, the classifier is obtained also by solving a system of linear equations rather than a QP. LS-STM is based on the tensor space, with tensor representation, the number of parameters estimated by LS-STM is less than the number of parameters estimated by LS-SVM, and avoids discarding a great deal of useful structural information. Experimental results on some benchmark datasets indicate that the performance of LS-STM is competitive in classification performance compared to LS-SVM.

KW - Alternating projection

KW - Least squares support tensor machine

KW - Least squares support vector machine

KW - Support tensor machine

KW - Tensor representation

UR - http://www.scopus.com/inward/record.url?scp=84902588683&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84902588683

SN - 9781849197137

T3 - 11th International Symposium on Operations Research and its Applications in Engineering, Technology and Management 2013, ISORA 2013

SP - 1

EP - 6

BT - 11th International Symposium on Operations Research and its Applications in Engineering, Technology and Management 2013, ISORA 2013

PB - Institution of Engineering and Technology

T2 - 11th International Symposium on Operations Research and Its Applications in Engineering, Technology and Management 2013, ISORA 2013

Y2 - 23 August 2013 through 25 August 2013

ER -