This paper analyzes the Fourier model reduction (FMR) method from a rational Krylov projection framework and shows how the FMR reduced model, which has guaranteed stability and a global error bound, can be computed in a numerically efficient and robust manner. By monitoring the rank of the Krylov subspace that underlies the FMR model, the projection framework also provides an improved criterion...

this paper considers the automatic design of fuzzy rule-basedclassification systems based on labeled data. the classification performance andinterpretability are of major importance in these systems. in this paper, weutilize the distribution of training patterns in decision subspace of each fuzzyrule to improve its initially assigned certainty grade (i.e. rule weight). ourapproach uses a punish...

Over the past decade considerable progress has been made towards the numerical solution of large-scale eigenvalue problems, particularly for nonsymmetric matrices. Krylov methods and variants of subspace iteration have been improved to the point that problems of the order of several million variables can be solved. The methods and software that have led to these advances are surveyed.

A randomsubsetmethod (RSM)with a newweighting scheme is proposed and investigated for linear regression with a large number of features. Weights of variables are defined as averages of squared values of pertaining t-statistics over fitted models with randomly chosen features. It is argued that such weighting is advisable as it incorporates two factors: a measure of importance of the variable wi...

A new version of the alternating directions implicit (ADI) iteration for the solution of large-scale Lyapunov equations is introduced. It generalizes the hitherto existing iteration, by incorporating tangential directions in the way they are already available for rational Krylov subspaces. Additionally, first strategies to adaptively select shifts and tangential directions in each iteration are...

Subspace analysis is one of popular multivariate data analysis methods, which has been widely used in pattern recognition. Typically data space belongs to very high dimension, but only a few principal components need to be extracted. In this paper, we present a fast sequential algorithm which behaves like expectation maximization (EM), for subspace analysis or tracking. In addition we also pres...

We propose a face difference model that decomposes face difference into three components, intrinsic difference, transformation difference, and noise. Using the face difference model and a detailed subspace analysis on the three components we develop a unified framework for subspace analysis. Using this framework we discover the inherent relationship among different subspace methods and their un...

Subspace clustering addresses an important problem in clustering multi-dimensional data. In sparse multi-dimensional data, many dimensions are irrelevant and obscure the cluster boundaries. Subspace clustering helps by mining the clusters present in only locally relevant subsets of dimensions. However, understanding the result of subspace clustering by analysts is not trivial. In addition to th...

This paper aims to address the face recognition problem with a wide variety of views. We proposed a tensor subspace analysis and view manifold modeling based multi-view face recognition algorithm by improving the TensorFace based one. Tensor subspace analysis is applied to separate the identity and view information of multi-view face images. To model the nonlinearity in view subspace, a novel v...

Linear Discriminant Analysis (LDA) often suffers from the small sample size problem when dealing with high dimensional face data. Random subspace can effectively solve this problem by random sampling on face features. However, it remains a problem how to construct an optimal random subspace for discriminant analysis and perform the most efficient discriminant analysis on the constructed random ...