Multiple kernel spectral regression for dimensionality reduction

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 incorporate multiple kernel learning (mkl) into sr for dimensionality reduction. the proposed approach (termed mkl-sr) seeks an embedding function in the reproducing kernel hilbert 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 proposed mkl-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. © 2013 bing liu et al.