Subspace Learning And Its Application To Image Set Classification

As an effective tool for high dimensional data analysis,subspace learning has been widely applied in many machine learning and computer vision tasks.From unsupervised dimension reduction to supervised discriminant analysis,from multiple local structures mining to cross-domain knowledge sharing and from face recognition to motion seg-mentation,subspace learning plays an important role in these fields.Among its many applications,there is a kind of problem which recently has drawn attention of researcher-s,which is image set classification.Unlike traditional classification techniques based on a single image,image set classification techniques are suitable for dealing with those objects with internal variations,such as video clips,multi-view object images,etc.An image set not only can provide rich information about an object,but also can simplify classification procedure and alleviate labelling burden.The structure characteristics of a subspace make it very suitable for modeling an image set.At present,image set classi-fication methods based on subspace have following issues.Firstly,due to the complex structure of an image set,it is insufficient to model a set via a single subspace.Secondly,most methods consider the pairwise set distance learning which neglect the collaboration among image sets.Especially for the case that a set does not contain enough images,which would produce a large measuring error.Thirdly,when a set is taken as a point on a Riemannian manifold,manifold learning could greatly expand the scope of the s-tudy of image set classification.However,the heterogeneity of image sets makes a single manifold could not fully characterize the structure of the sets.Fourthly,it is common to employ kernel methods to perform dimension reduction on the manifolds.But we can-not easily obtain the explicit representation of low-dimensional manifolds through these methods,and meanwhile,they may cause much computational burden.To address these problems,the main works of this paper include:(1)For the complex structure of image sets,we propose a subspace clustering method based on constrained elastic-net to recover multiple subspaces structure of a set.In this method,the self-reconstruction coefficients are used to measure data simi-larity,then a spectral clustering method is utilized to generate the final clustering assignment.In order to obtain more robust coefficients,a combination of a l1 nor-m and a Frobenius norm is induced here.Moreover,a weighting scheme based on shape interaction matrix is proposed to enhance the intra-subspace compactness and strengthen the inter-subspace separability.(2)For data representation under multiple sets scenario,we propose a set represen-tation method based on a group collaborative penalty.In this method,several subspaces are firstly extracted from training image sets via a subspace cluster-ing method.And then point-to-sets representations(PSsR)of individual training images and set-to-sets representations(SSsR)of testing image sets are obtained.The former can compensate for the performance degeneration caused by lacking of samples in one set,and the latter can enhance the robustness of representation of testing sets and improve the efficiency of the testing phase.(3)For the problem of insufficient representation of image sets using a single manifold,a framework of semi-supervised learning on multi-Riemannian manifolds(SSMM)is proposed.This framework is consist of a group of semi-supervised learners on different manifolds.It takes advantage of the complementarity among manifolds.Unlike the traditional graph-based semi-supervised learning methods,in which the graph building and label propagation are divided into two parts.This framework can not only provide the graph on each manifold for label inference,but also bring back the supervised information gathered from different manifolds to guide the graphs generation.(4)For the problem of discriminative manifold learning,based on the triplet loss,we propose an adaptive cluster triplet loss(ACTL).This method considers two types of distance,i.e.,the distance between cluster centers and the distance between clus-ter center and samples.The former is used to enhance the robustness of constraints and reduce the number of them.The latter is used to replace the margin parameter which is hardly assigned in the original triplet loss.The effectiveness of the frame-work is verified on different manifolds,such as symmetric positive definite(SPD)matrices manifold and Euclidean space.