Related papers: EqRank: A Self-Consistent Equivalence Relation on …

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…

Time evolution of the classification scheme generated by the EqRank algorithm is studied with hep-th citation graph as an example. Intuitive expectations about evolution of an adequate classification scheme for a growing set of objects are…

A vertex ranking of a graph is an assignment of ranks (or colors) to the vertices of the graph, in such a way that any simple path connecting two vertices of equal rank, must contain a vertex of a higher rank. In this paper we study a…

In this paper we propose a graph-community detection approach to identify cross-document relationships at the topic segment level. Given a set of related documents, we automatically find these relationships by clustering segments with…

In graph theory a partition of the vertex set of a graph is called equitable if for all pairs of cells all vertices in one cell have an equal number of neighbours in the other cell. Considering the implications for the adjacency matrix one…

Network-valued data are encountered in a wide range of applications and pose challenges in learning due to their complex structure and absence of vertex correspondence. Typical examples of such problems include classification or grouping of…

The bipartite graph is a ubiquitous data structure that can model the relationship between two entity types: for instance, users and items, queries and webpages. In this paper, we study the problem of ranking vertices of a bipartite graph,…

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…

Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct…

As machine learning has become more prevalent, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates…

We propose a novel graph-based approach for constructing concept hierarchy from a large text corpus. Our algorithm, GraBTax, incorporates both statistical co-occurrences and lexical similarity in optimizing the structure of the taxonomy. To…

Graph clustering is a longstanding research topic, and has achieved remarkable success with the deep learning methods in recent years. Nevertheless, we observe that several important issues largely remain open. On the one hand, graph…

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…

Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…

Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…

This paper investigates the application of consensus clustering and meta-clustering to the set of all possible partitions of a data set. We show that when using a "complement" of Rand Index as a measure of cluster similarity, the…

We propose a hierarchical correlation clustering method that extends the well-known correlation clustering to produce hierarchical clusters applicable to both positive and negative pairwise dissimilarities. Then, in the following, we study…

We study the complexity of finding an optimal hierarchical clustering of an unweighted similarity graph under the recently introduced Dasgupta objective function. We introduce a proof technique, called the normalization procedure, that…

In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…