Anita Keszler

A mixed graph model for community detection

A mixed graph theoretic model is proposed for finding communities in a social network. Information on the habits (shopping habits, free time activities) is considered to be known at least for part of the society. The presented model is based on applying parallelly a standard and a bipartite graph. Compared to previous methods, the introduced algorithm has the advantage of noise-tolerance and is suitable independently of the size of the clusters in the graph. Clusters in the dataset tend to form dense subgraphs in both graph models. The idea is to speed up cluster core mining by a modified MST algorithm. Noise in the dataset is defined as missing information on a persons habits. Clustering noisy data is done by using a bipartite graph and fuzzy membership functions. The proposed algorithm can be used for predicting the missing data estimated on the available information patterns. The presented mixed graph model might also be used for image processing tasks.

Dense subgraph mining with a mixed graph model

In this paper we introduce a graph clustering method based on dense bipartite subgraph mining. The method applies a mixed graph model (both standard and bipartite) in a three-phase algorithm. First a seed mining method is applied to find seeds of clusters, the second phase consists of refining the seeds, and in the third phase vertices outside the seeds are clustered. The method is able to detect overlapping clusters, can handle outliers and applicable without restrictions on the degrees of vertices or the size of the clusters. The running time of the method is polynomial. A theoretical result is introduced on density bounds of bipartite subgraphs with size and local density conditions. Test results on artificial datasets and social interaction graphs are also presented.

The appearance of the giant component in descriptor graphs and its application for descriptor selection

The paper presents a random graph based analysis approach for evaluating descriptors based on pairwise distance distributions on real data. Starting from the Erdős-Renyi model the paper presents results of investigating random geometric graph behaviour in relation with the appearance of the giant component as a basis for choosing descriptors based on their clustering properties. Experimental results prove the existence of the giant component in such graphs, and based on the evaluation of their behaviour the graphs, the corresponding descriptors are compared, and validated in proof-of-concept retrieval tests.

Component evolution analysis in descriptor graphs for descriptor ranking

Abstract This paper presents a method based on graph behaviour analysis for the evaluation of descriptor graphs (applied to image/video datasets) for descriptor performance analysis and ranking. Starting from the Erdős–Renyi model on uniform random graphs, the paper presents results of investigating random geometric graph behaviour in relation with the appearance of the giant component as a basis for ranking descriptors based on their clustering properties. We analyse the phase transition and the evolution of components in such graphs, and based on their behaviour, the corresponding descriptors are compared, ranked, and validated in retrieval tests. The goal is to build an evaluation framework where descriptors can be analysed for automatic feature selection.

On the distance of databases

In the present paper a distance concept of databases is investigated. Two database instances are of distance 0, if they have the same number of attributes and satisfy exactly the same set of functional dependencies. This naturally leads to the poset of closures as a model of changing database. The distance of two databases (closures) is defined to be the distance of the two closures in the Hasse diagram of that poset. We determine the diameter of the poset and show that the distance of two closures is equal to the natural lower bound, that is to the size of the symmetric difference of the collections of closed sets. We also investigate the diameter of the set of databases with a given system of keys. Sharp upper bounds are given in the case when the minimal keys are 2 (or r)-element sets.

Noise Tolerant Community Detection Using a Mixed Graph Model

In this paper a new concept is proposed for finding communities in a social network based on a mixed graph theoretic model of a standard and a bipartite graph. Compared to previous methods the introduced algorithm has the advantage of noise-tolerance and is applicable independently of the size of the clusters in the graph. The cluster core-mining method is based on a modified MST algorithm. Clustering incomplete data is done by using bipartite graphs and fuzzy membership functions.

Matching Matchings

This paper presents the first steps toward a graph comparison method based on matching matchings, or in other words, comparison of independent edge sets in graphs. The novelty of our approach is to use matchings for calculating distance of graphs in case of edge-colored graphs. This idea can be used as a preprocessing step of graph querying applications, to speed up exact and inexact graph matching methods. We introduce the notion of colored matchings and prove some properties of them in edge colored complete graphs and complete bipartite graphs in case of two colors.