We present an implementation of the Normalized Cuts method for the solution of the image segmentation problem on polygonal grids. We show that in the presence of rounding errors the eigenvector corresponding to the k-th smallest eigenvalue of the generalized graph Laplacian is likely to contain more than k nodal domains. It follows that the Fiedler vector alone is not always suitable for graph ...

Abstruct-Pisarenko’s harmonic retrieval (PHR) method is perhaps the first eigenstructure based spectral estimation technique. The basic step in this method is the computation of eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix of the underlying data. In this paper, we recast a known constrained minimization formulation for obtaining this eigenvector into the neu...

This paper describes a spectral method for graph-matching. We adopt a graphical models viewpoint in which the graph adjacency matrix is taken to represent the transition probability matrix of a Markov chain. The nodeorder of the steady state random walk associated with this Markov chain is determined by the co-efficent order of the leading eigenvector of the adjacency matrix. We match nodes in ...

This paper provides a general approach to the computation, for sufficiently regular multiresolution analyses, of scaling functions and wavelets and their derivatives. Two distinct iterative schemes are used to determine the multiresolution functions, the so-called ‘cascade’ algorithm and an eigenvector-based method. We present a novel development of these procedures which not only encompasses b...

Control of permanent magnetic actuators is not an easy task because of the presence of the nonlinear quadratic terms of the currents. In order to achieve a suitable controlled dynamics canceling the effect of the nonlinearity, a new control strategy has been conceived. The proposed strategy combines the geometric eigenvector concept through a pre-compensation action and a Model Predictive Contr...

This paper presents the applications of Eigenvalues and Eigenvectors (as part of spectral decomposition) to analyze the bipartivity index of graphs as well as to predict the set of vertices that will constitute the two partitions of graphs that are truly bipartite and those that are close to being bipartite. Though the largest eigenvalue and the corresponding eigenvector (called the principal e...

Algorithms such as Kleinberg’s HITS algorithm, the PageRank algorithm of Brin and Page, and the SALSA algorithm of Lempel and Moran use the link structure of a network of web pages to assign weights to each page in the network. The weights can then be used to rank the pages as authoritative sources. These algorithms share a common underpinning; they find a dominant eigenvector of a nonnegative ...

Due to the significant increment of the volume of interactions among the population, probabilistic process on complex network can be often utilized to analyse diffusion phenomena in the society, then a number of researchers have studied especially from the perspectives of social network analysis, computer virus spread study, and epidemics study. So far, it has been believed that the largest eig...

We give faster algorithms and improved sample complexities for the fundamental problem of estimating the top eigenvector. Given an explicit matrix A ∈ Rn×d, we show how to compute an approximate top eigenvector of A>A in time Õ ([ nnz(A) + d sr(A) gap2 ] · log 1/ ) . Here nnz(A) is the number of nonzeros in A, sr(A) is the stable rank, and gap is the relative eigengap. We also consider an onlin...

Recent developments in network theory have allowed for the study of the structure and function of the human brain in terms of a network of interconnected components. Among the many nodes that form a network, some play a crucial role and are said to be central within the network structure. Central nodes may be identified via centrality metrics, with degree, betweenness, and eigenvector centralit...