Ng–Jordan–Weiss (NJW) method is one of the most widely used spectral clustering algorithms. For a K clustering problem, this method partitions data using the largest K eigenvectors of the normalized affinity matrix derived from the dataset. It has been demonstrated that the spectral relaxation solution of K-way grouping is located on the subspace of the largest K eigenvectors. However, we find ...

In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors tensors is studied, which have found many applications in diverse areas. The main results are: (i) each (Z-)eigenvector/singular tuple a generic tensor nondegenerate, (ii) nonzero Z-eigenvector/singular an orthogonally decomposable nondegenerate.

The task of discovering natural groupings of input patterns, or clustering, is an important aspect machine learning and pattern analysis. In this paper, we study the widely-used spectral clustering algorithm which clusters data using eigenvectors of a similarity/affinity matrix derived from a data set. In particular, we aim to solve two critical issues in spectral clustering: (1) How to automat...

Phylogenetic Eigenvector Regression (PVR) is a fl exible comparative method that allows testing several hypotheses on phylogenetic signal and correlated evolution among traits. Selected phylogenetic eigenvectors extracted from a phylogenetic distance matrix among taxa allow representing their phylogenetic relatedness in a raw-data form (i.e. instead of a distance matrix) and can then be used as...

the analysis of cross-correlations is extensively applied for understanding of interconnections in stock markets. variety of methods are used in order to search stock cross-correlations including the random matrix theory (rmt), the principal component analysis (pca) and the hierachical ‎structures.‎ in ‎this work‎, we analyze cross-crrelations between price fluctuations of 20 ‎company ‎stocks‎‎...

Pairwise comparisons are used in a wide variety of decision situations where the importance alternatives should be measured on numerical scale. One popular method to derive priorities is based right eigenvector multiplicative pairwise comparison matrix. We consider two monotonicity axioms this setting. First, increasing an arbitrary entry matrix not allowed result counter-intuitive rank reversa...