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- Title
Multiple Kernel Spectral Regression for Dimensionality Reduction.
- Authors
Bing Liu; Shixiong Xia; Yong Zhou
- Abstract
Traditional manifold learning algorithms, such as locally linear embedding, Isomap, and Laplacian eigenmap, only provide the embedding results of the training samples. To solve the out-of-sample extension problem, spectral regression (SR) solves the problem of learning an embedding function by establishing a regression framework, which can avoid eigen-decomposition of dense matrices. Motivated by the effectiveness of SR,we incorporatemultiple kernel learning (MKL) into SR for dimensionality reduction. Theproposed approach (termedMKL-SR) seeks an embedding function in the Reproducing KernelHilbert Space (RKHS) induced by the multiple base kernels. An MKL-SR algorithm is proposed to improve the performance of kernel-based SR (KSR) further. Furthermore, the proposedMKL-SR algorithm can be performed in the supervised, unsupervised, and semi-supervised situation. Experimental results on supervised classification and semi-supervised classification demonstrate the effectiveness and efficiency of our algorithm.
- Subjects
KERNEL (Mathematics); SPECTRAL theory; REGRESSION analysis; DIMENSION reduction (Statistics); MACHINE learning; EMBEDDINGS (Mathematics); LAPLACIAN matrices
- Publication
Journal of Applied Mathematics, 2013, p1
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/2013/427462