Convergence results are provided for inexact inverse subspace iteration applied to the problem of finding the invariant subspace associated with a small number of eigenvalues of a large sparse matrix. These results are illustrated by the use of block-GMRES as the iterative solver. The costs of the inexact solves are measured by the number of inner iterations needed by the iterative solver at ea...

Linear discriminant analysis (LDA) is a well-known scheme for supervised subspace learning. It has been widely used in the applications of computer vision and pattern recognition. However, an intrinsic limitation of LDA is the sensitivity to the presence of outliers, due to using the Frobenius norm to measure the inter-class and intra-class distances. In this paper, we propose a novel rotationa...

Bayesian subspace analysis has been successfully applied in face recognition. However, it suffers from its operating on a whole face difference and using one global linear subspace to represent the similarity model. We develop a novel approach to address these problems. The proposed method operates directly on a set of partitioned local regions of the global face differences, and a separate Gau...

Subspace learning seeks a low dimensional representation of data that enables accurate reconstruction. However, in many applications, data is obtained from multiple sources rather than a single source (e.g. an object might be viewed by cameras at different angles, or a document might consist of text and images). The conditional independence of separate sources imposes constraints on their share...

HAMID HASSANPOUR School of Information Technology and Computer Engineering, Shahrood University of Technology. ___________________________________________________________________________________ Abstract: In this paper, a new method is presented for noise reduction in signal using partial differential equations. In this approach, the signal is initially represented as a matrix. Then using singu...

In face recognition, LDA often encounters the so-called small sample size (SSS) problem, also known as curse of dimensionality. This problem occurs when the dimensionality of the data is quite large in comparison to the number of available training images. One of the approaches for handling this situation is the subspace LDA. It is a two-stage framework: it first uses PCA-based method for dimen...

We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite tree structure associated with the underlying Hilbert space. These shifts arise naturally through weighted versions of certain representations of the Cuntz C...

We construct generalizations of the Calogero-Sutherland-Moser system by appropriately reducing a classical Calogero model by a subset of its discrete symmetries. Such reductions reproduce all known variants of these systems, including some recently obtained generalizations of the spin-Sutherland model, and lead to further generalizations of the elliptic model involving spins with SU(n) non-inva...