TY - GEN
T1 - Learning the optimal neighborhood kernel for classification
AU - Liu, Jun
AU - Chen, Jianhui
AU - Chen, Songcan
AU - Ye, Jieping
PY - 2009
Y1 - 2009
N2 - Kernel methods have been applied successfully in many applications. The kernel matrix plays an important role in kernel-based learning methods, but the "ideal" kernel matrix is usually unknown in practice and needs to be estimated. In this paper,we propose to directly learn the "ideal" kernel matrix (called the optimal neighborhood kernel matrix) from a pre-specified kernel matrix for improved classification performance. We assume that the pre-specified kernel matrix generated from the specific application is a noisy observation of the ideal one. The resulting optimal neighborhood kernel matrix is shown to be the summation of the pre-specified kernel matrix and a rank-one matrix. We formulate the problem of learning the optimal neighborhood kernel as a constrained quartic problem, and propose to solve it using two methods: level method and constrained gradient descent. Empirical results on several benchmark data sets demonstrate the efficiency and effectiveness of the proposed algorithms.
AB - Kernel methods have been applied successfully in many applications. The kernel matrix plays an important role in kernel-based learning methods, but the "ideal" kernel matrix is usually unknown in practice and needs to be estimated. In this paper,we propose to directly learn the "ideal" kernel matrix (called the optimal neighborhood kernel matrix) from a pre-specified kernel matrix for improved classification performance. We assume that the pre-specified kernel matrix generated from the specific application is a noisy observation of the ideal one. The resulting optimal neighborhood kernel matrix is shown to be the summation of the pre-specified kernel matrix and a rank-one matrix. We formulate the problem of learning the optimal neighborhood kernel as a constrained quartic problem, and propose to solve it using two methods: level method and constrained gradient descent. Empirical results on several benchmark data sets demonstrate the efficiency and effectiveness of the proposed algorithms.
UR - http://www.scopus.com/inward/record.url?scp=77958559950&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77958559950&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:77958559950
SN - 9781577354260
T3 - IJCAI International Joint Conference on Artificial Intelligence
SP - 1144
EP - 1149
BT - IJCAI-09 - Proceedings of the 21st International Joint Conference on Artificial Intelligence
PB - International Joint Conferences on Artificial Intelligence
T2 - 21st International Joint Conference on Artificial Intelligence, IJCAI 2009
Y2 - 11 July 2009 through 16 July 2009
ER -