Related papers: Characterizing Properties for Q-Clustering

Quality assessments of models in unsupervised learning and clustering verification in particular have been a long-standing problem in the machine learning research. The lack of robust and universally applicable cluster validity scores often…

In Network Science node neighbourhoods, also called ego-centered networks have attracted large attention. In particular the clustering coefficient has been extensively used to measure their local cohesiveness. In this paper, we show how,…

We study the structure of loops in networks using the notion of modulus of loop families. We introduce a new measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected…

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…

Components of complex systems are often classified according to the way they interact with each other. In graph theory such groups are known as clusters or communities. Many different techniques have been recently proposed to detect them,…

We present a new characterization of $k$-trees based on their reduced clique graphs and $(k+1)$-line graphs, which are block graphs. We explore structural properties of these two classes, showing that the number of clique-trees of a…

With the rapid development of online social media, online shopping sites and cyber-physical systems, heterogeneous information networks have become increasingly popular and content-rich over time. In many cases, such networks contain…

Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…

Clustering is a widely used technique in data mining applications for discovering patterns in underlying data. Most traditional clustering algorithms are limited to handling datasets that contain either numeric or categorical attributes.…

We propose a multi-phase approach to explore network structures. In this method, structure analysis is not carried out on the observed network directly. Instead, certain similarity measures of the nodes are derived from the network firstly,…

High-level classification algorithms focus on the interactions between instances. These produce a new form to evaluate and classify data. In this process, the core is the complex network building methodology because it determines the…

We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering…

Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community. While being…

The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…

Motivated by the fact that entities in a social network or biological system often interact by exchanging information, we propose an efficient info-clustering algorithm that can group entities into communities using a parametric max-flow…

Gomory-Hu (GH) Trees are a classical sparsification technique for graph connectivity. It is one of the fundamental models in combinatorial optimization which also continually finds new applications, most recently in social network analysis.…

We develop the Blooming Tree Algorithm, a new technique that uses spectroscopic redshift data alone to identify the substructures and the surrounding groups of galaxy clusters, along with their member galaxies. Based on the estimated…

With the explosive growth of multi-source data, multi-view clustering has attracted great attention in recent years. Most existing multi-view methods operate in raw feature space and heavily depend on the quality of original feature…

Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…

Two natural and widely used representations for the community structure of networks are clusterings, which partition the vertex set into disjoint subsets, and layouts, which assign the vertices to positions in a metric space. This paper…