Learning Robust and Discriminative Subspace With Low-Rank Constraints

IEEE Transactions on Neural Networks and Learning SystemsThe article of record as published may be found at http://dx.doi.org/10.1109/tnnls.2015.2464090In this paper, we aim at learning robust and discriminative subspaces from noisy data. Subspace learning is widely used in extracting discriminative features for classifica- tion. However, when data are contaminated with severe noise, the performance of most existing subspace learning methods would be limited. Recent advances in low-rank modeling provide effective solutions for removing noise or outliers contained in sample sets, which motivates us to take advantage of low-rank constraints in order to exploit robust and discriminative subspace for classification. In particular, we present a discriminative subspace learning method called the supervised regularization- based robust subspace (SRRS) approach, by incorporating the low-rank constraint. SRRS seeks low-rank representations from the noisy data, and learns a discriminative subspace from the recovered clean data jointly. A supervised regularization function is designed to make use of the class label information, and therefore to enhance the discriminability of subspace. Our approach is formulated as a constrained rank-minimization problem. We design an inexact augmented Lagrange multiplier optimization algorithm to solve it. Unlike the existing sparse representation and low-rank learning methods, our approach learns a low-dimensional subspace from recovered data, and explicitly incorporates the supervised information. Our approach and some baselines are evaluated on the COIL-100, ALOI, Extended YaleB, FERET, AR, and KinFace databases. The exper- imental results demonstrate the effectiveness of our approach, especially when the data contain considerable noise or variations.Funded by Naval Postgraduate SchoolNational Science Foundation Computer and Network SystemsONR Young InvestigatorOffice of Naval ResearchU.S. Army Research Office Young Investigato

Exploiting Low-dimensional Structures to Enhance DNN Based Acoustic Modeling in Speech Recognition

We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces. To that end, the training posteriors are used for dictionary learning and sparse coding. Sparse representation of the test posteriors using this dictionary enables projection to the space of training data. Relying on the fact that the intrinsic dimensions of the posterior subspaces are indeed very small and the matrix of all posteriors belonging to a class has a very low rank, we demonstrate how low-dimensional structures enable further enhancement of the posteriors and rectify the spurious errors due to mismatch conditions. The enhanced acoustic modeling method leads to improvements in continuous speech recognition task using hybrid DNN-HMM (hidden Markov model) framework in both clean and noisy conditions, where upto 15.4% relative reduction in word error rate (WER) is achieved

Disturbance Grassmann Kernels for Subspace-Based Learning

In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers, e.g., Support Vector Machines (SVMs). However, the existing discriminative algorithms mostly ignore the instability of subspaces, which would cause the classifiers misled by disturbed instances. Thus we propose considering all potential disturbance of subspaces in learning processes to obtain more robust classifiers. Firstly, we derive the dual optimization of linear classifiers with disturbance subject to a known distribution, resulting in a new kernel, Disturbance Grassmann (DG) kernel. Secondly, we research into two kinds of disturbance, relevant to the subspace matrix and singular values of bases, with which we extend the Projection kernel on Grassmann manifolds to two new kernels. Experiments on action data indicate that the proposed kernels perform better compared to state-of-the-art subspace-based methods, even in a worse environment.Comment: This paper include 3 figures, 10 pages, and has been accpeted to SIGKDD'1