Related papers: Tangles and Hierarchical Clustering
One of the main challenges for hierarchical clustering is how to appropriately identify the representative points in the lower level of the cluster tree, which are going to be utilized as the roots in the higher level of the cluster tree…
Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet. In this paper, we propose a…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
When some 'entities' are related by the 'features' they share they are amenable to a bipartite network representation. Plant-pollinator ecological communities, co-authorship of scientific papers, customers and purchases, or answers in a…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
Finding densely connected subsets of vertices in an unsupervised setting, called clustering or community detection, is one of the fundamental problems in network science. The edge clustering approach instead detects communities by…
Hierarchical clustering is a common algorithm in data analysis. It is unique among many clustering algorithms in that it draws dendrograms based on the distance of data under a certain metric, and group them. It is widely used in all areas…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
Robertson and Seymour proved two fundamental theorems about tangles in graphs: the tree-of-tangles theorem, which says that every graph has a tree-decomposition such that distinguishable tangles live in different nodes of the tree, and the…
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
We show how an image can, in principle, be described by the tangles of the graph of its pixels. The tangle-tree theorem provides a nested set of separations that efficiently distinguish all the distinguishable tangles in a graph. This…
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…
The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…
Graph clustering is a fundamental and challenging task in the field of graph mining where the objective is to group the nodes into clusters taking into consideration the topology of the graph. It has several applications in diverse domains…
Hierarchical clustering over graphs is a fundamental task in data mining and machine learning with applications in domains such as phylogenetics, social network analysis, and information retrieval. Specifically, we consider the recently…
This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping…