We present an overview of eigen analysis methods and their applications to network analysis. We consider several network analysis programs/procedures (Correspondence Analysis, NEGOPY, CONCOR, CONVAR, Bonacich centrality) that are at their core eigendecomposition methods. We discuss the various matrix representations of networks used by these procedures and we give particular attention to a vari...

Eigen decomposition is a central mathematical tool in many pattern recognition and machine learning techniques. However, it becomes computationally infeasible in the presence of a large set of high-dimensional samples. Moreover, in highly dynamic domains with a continual supply of new samples, an incremental approach that keeps on updating the eigen decomposition will be more desirable than the...

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

We map the Eigen model of biological evolution [Naturwissenschaften 58, 465 (1971)] into a quantum spin model with non-Hermitian Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We also study a simple case of dynamic fitness function.

We show that functions which are invariant for suitable product semigroups (one of which is a quasi-Poisson semigroup on a general state space) decompose into a singular eigen-function and a mixture of products of minimal eigen-functions. Mathematics Subject Classifications (2000): 31C20, 35C15, 47G20, 60J45, 46A55.

People employ the function-on-function regression to model relationship between two stochastic processes. Fitting this model, widely used strategies include functional partial least squares algorithms which typically require iterative eigen-decomposition. Here we introduce a route of based upon Krylov subspace. Our can be expressed in forms equivalent each other exact arithmetic: One is non-ite...

This paper presents an efficient face recognition system which can handle partial occlusion in both training and test image sets. We hybridize Gabor filter with Eigen faces which make use of localization effect of Gabor filter and whole appearance effect of Eigen faces. It has been tested on AR database which contains naturally occluded face images.

The eigen fuzzy set of a given fuzzy relation often corresponds to an occurrence of invariability in natural sciences. By determining the fuzzy relations as connections between pairs of symptoms we utilize the greatest and the least eigen fuzzy sets in order to find the estimates of the medicine effectiveness levels.

With the advancement in geospatial data acquisition technology, large sizes of digital data are being collected for our world. These include airand space-borne imagery, LiDAR data, sonar data, terrestrial laser-scanning data, etc. LiDAR sensors generate huge datasets of point of multiple returns. Because of its large size, LiDAR data has costly storage and computational requirements. In this ar...