Abstract: Subspace learning is an important research subject in the field of feature extraction.It maps the original data into a low-dimensional subspace through a linear or nonlinear transformation,and preserves the geometric structure and useful information of the original data as much as possible in this subspace.The performance of subspace learning mainly depends on the design of similarity measure and the graph construction for feature embedding.Aiming at the two issues,a novel kernel-preserving embedding based subspace learning(KESL) method is proposed,which can adaptively learn the similarity information from data and construct the kernel-preserving graph.First,to tackle the problem that the traditional dimension reduction methods cannot preserve the inner structure of high-dimensional nonlinear data,our algorithm introduces the kernel function and minimizes the reconstruction error of samples,which is beneficial for mining the data structural relationship for classification.Then,aiming at the limitation that existing graph-based subspace learning methods mainly concern the similarity information of the samples within a class,our algorithm uses the learned similarity matrices to construct intra-class and inter-class graphs,respectively.Thus,in the projected subspace,the kernel-preserving relationship of the samples in the same class can be strengthened,while the kernel-preserving relationship of the samples from different classes can be largely inhibited.Finally,through the joint optimization of kernel preserving matrix and graph embedding,the desired projection under the optimal representation can be dynamically solved.Expe-rimental results on several datasets show that the proposed algorithm is competitive to the state-of-the-art subspace learning algorithms in various classification tasks.

Key words: Graph construction, Kernel-preserving embedding, Similarity learning, Subspace learning