Spectral graph theory

About: Spectral graph theory is a research topic. Over the lifetime, 1334 publications have been published within this topic receiving 77373 citations.

Relational graph clustering based on spectral coefficient angle

Abstract: This paper introduces a relational graph representation method using the angle between spectral coefficient vectors. A relational graph clustering system builds on this presentation method. The system adopts fuzzy C-mean (FCM) as clustering algorithm. FCM exerts on the pattern space which embedded by locality preserving projections (LPP). The pattern space obtains from Laplacian matrix constructed by the corner points oriented graph from image sequence. After matrix decomposition at hand, the angle between spectral coefficients vectors as spectral features are computed through eigen value and eigen vectors of it. These features can describe the distribution and relationship of all graph nodes. Experiment shows that the spectral features of the angle between spectral coefficient vectors of Laplacian graph represent image sequence correctly and graph clustering in the feature pattern space is valid.

Graph representations using adjacency matrix transforms for clustering

Abstract: This paper is meant as a proof of concept regarding the application of standard 2D signal representation and feature extraction tools that have wide use in their respective fields to graph related pattern recognition tasks such as, in this case, clustering. By viewing the adjacency matrix of a graph as a 2-dimensional signal, we can apply 2D Discrete Cosine Transform (DCT) to it and use the relation between the adjacency matrix and the values of the DCT bases in order to cluster nodes into strongly connected components. By viewing the adjacency matrices of multiple graphs as feature vectors, we can apply Principal Components Analysis (PCA) to decorrelate them and achieve better clustering performance. Experimental results on synthetic data indicate that there is potential in the use of such techniques to graph analysis.

A Thermodynamics Approach to Graph Similarity

Abstract: In this paper, we describe the use of concepts from the areas of spectral-graph theory, kernel methods and differential geometry for the purposes of recovering a measure of similarity between pairs of graphical structures. To do this, we commence by relating each of the graphs under study to a Riemannian manifold through the use of the graph Laplacian and the heat operator. We do this by making use of the heat kernel and the set of initial conditions for the space of functions associated to the Laplace-Beltrami operator. With these ingredients, we make use of the first law of thermodynamics to recover the thermal energy associated to the conduction of heat through the graph. Thus, the problem of recovering a measure of similarity between pairs of graphs becomes that of computing the difference in their thermal energies. We illustrate the utility of the similarity metric recovered in this way for purposes of content-based image database indexing and retrieval.

Increasing statistical power in medical image analysis

Abstract: In this paper, we present a novel method for estimating the effective number of independent variables in imaging applications that require multiple hypothesis testing. The method increases the statistical power of the results by refuting the assumption of independence among variables, while keeping the probability of false positives low. It is based on the spectral graph theory, in which the variables are seen as the vertices of a complete undirected graph and the correlation matrix as the adjacency matrix that weights its edges. By computing the eigenvalues of the correlation matrix, it is possible to obtain valuable information about the dependence levels among the variables of the problem. The method is compared to other available models and its effectiveness illustrated in a case study on the morphology of the human corpus callosum.

Facial Expression Analysis Based on Graph Spectral Decomposition

Abstract: In this paper explore how to use spectral methods of geometry structural graph for analyzing facial expression and clustering in the pattern-space.Use the leading eigenvectors of the weighted graph adjacency matrix to define eigenmodes of the adjacency matrix.For each eigenmode,compute vectors of spectral properties.It includes the leading inter-mode adjacency matrices.Embed these vectors in a pattern-space using multidimensional scaling on the norm for pairs of patten vectors.Illustrate the utility of the embedding methods representing the arrangement of facial expression of dissimilar human face in the pattern-space.