Related papers: Hierarchical Clustering for Finding Symmetries and…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the…
One way of getting a better view of data is using frequent patterns. In this paper frequent patterns are subsets that occur a minimal number of times in a stream of itemsets. However, the discovery of frequent patterns in streams has always…
Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and…
The problem of hierarchical clustering items from pairwise similarities is found across various scientific disciplines, from biology to networking. Often, applications of clustering techniques are limited by the cost of obtaining…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods that, based on the dissimilarity structure, output hierarchical clusters, i.e., a family of nested…
Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of…
Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…
We bring together topological data analysis, applied category theory, and machine learning to study multiparameter hierarchical clustering. We begin by introducing a procedure for flattening multiparameter hierarchical clusterings. We…
Symmetry is usually defined via transformations described by a (higher) group. But a symmetry really corresponds to an algebra of local symmetric operators, which directly constrains the properties of the system. In this paper, we point out…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
The study of irreducible higher-order interactions has become a core topic of study in complex systems. Two of the most well-developed frameworks, topological data analysis and multivariate information theory, aim to provide formal tools…
We present Clusterplot, a multi-class high-dimensional data visualization tool designed to visualize cluster-level information offering an intuitive understanding of the cluster inter-relations. Our unique plots leverage 2D blobs devised to…
Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…
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 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…
A new depth-based clustering procedure for directional data is proposed. Such method is fully non-parametric and has the advantages to be flexible and applicable even in high dimensions when a suitable notion of depth is adopted. The…