In an era where accumulating data is easy and storing it inexpensive, feature selection plays a central role in helping to reduce the high-dimensionality of huge amounts of otherwise meaningless data. In this paper, we propose a graph-based method for feature selection that ranks features by identifying the most important ones into arbitrary set of cues. Mapping the problem on an affinity graph...

We consider N×N Hermitian or symmetric random matrices with independent entries. The distribution of the (i, j)-th matrix element is given by a probability measure νij whose first two moments coincide with those of the corresponding Gaussian ensemble. We prove that the joint probability distribution of the components of eigenvectors associated with eigenvalues close to the spectral edge agrees ...

Networks of social relations can be represented by graphs and socioor adjacency-matrices and their structure can be analyzed using different concepts, one of them called centrality. We will provide a new formalization of a “node-centrality” which leads to some properties a measure of centrality has to satisfy. These properties allow to test given measures, for example measures based on degree, ...

Introduction. Functional magnetic resonance data acquired in a task-absent condition (``resting state'') require new data analysis techniques that do not depend on an activation model. Standard methods use either correlations with pre-specified seed regions or independent component analysis, both of which require assumptions about the source (seed-based) or validity (ICA) of a network. In this ...

We give a condition ensuring that the operators in a nilpotent Lie algebra of linear operators on a finite dimensional vector space have a common eigenvector. Introduction Throughout this paper V is a vector space of positive dimension over a field f and g is a nilpotent Lie algebra over f of linear operators on V . An element u ∈ V is an eigenvector for S ⊂ g if u is an eigenvector for every o...

Convectively coupled equatorial waves (CCEWs) are often identified by space–time filtering techniques that make use of the eigenvalues of linear shallow water theory. Here, instead, a method is presented for identifying CCEWs by projection onto the eigenvectors of the theory. This method does not use space–time filtering; instead, wave signals corresponding to the first baroclinic Kelvin, Rossb...

This study is motivated by a need to effectively determine the difference between a system fault and normal system operation under parametric uncertainty using eigenstructure analysis. This involves computational robustness of eigenvectors in linear state space systems dependent upon uncertain parameters. The work involves the development of practical algorithms which provide for computable rob...

Space and time are two critical components of many real world systems. For this reason, analysis of anomalies in spatiotemporal data has been a great of interest. In this work, application of tensor decomposition and eigenspace techniques on spatiotemporal hotspot detection is investigated. An algorithm called SST-Hotspot is proposed which accounts for spatiotemporal variations in data and dete...

Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.

This paper generalizes the well-known identity which relates the last components of the eigenvectors of a symmetric matrix A to the eigenvalues of A and of the matrix An−1, obtained by deleting the last row and column of A. The generalizations relate to matrices and to Sturm–Liouville equations.