相关论文: Natural clustering: the modularity approach

A parameterisation of generalised network clustering, in the form of four-motif prevalences, is presented. This involves three real parameters that are conditional on one- two- and three-motif prevalences. Interpretations of these real…

We present a novel clustering approach for moving object trajectories that are constrained by an underlying road network. The approach builds a similarity graph based on these trajectories then uses modularity-optimization hiearchical graph…

We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or $\textit{modal-sets}$, of…

Clustering algorithms may unintentionally propagate or intensify existing disparities, leading to unfair representations or biased decision-making. Current fair clustering methods rely on notions of fairness that do not capture any…

Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in…

In this paper we propose a measure of clustering quality or accuracy that is appropriate in situations where it is desirable to evaluate a clustering algorithm by somehow comparing the clusters it produces with ``ground truth' consisting of…

An approach to improve neural network interpretability is via clusterability, i.e., splitting a model into disjoint clusters that can be studied independently. We define a measure for clusterability and show that pre-trained models form…

Ecological systems can be seen as networks of interactions between individual, species, or habitat patches. A key feature of many ecological networks is their organization into modules, which are subsets of elements that are more connected…

Modularity is a general principle present in many fields. It offers attractive advantages, including, among others, ease of conceptualization, interpretability, scalability, module combinability, and module reusability. The deep learning…

Study of the cluster- or community structure of complex networks makes an important contribution to the understanding of networks at a functional level. Despite the many efforts, no definition of community has been agreed on and important…

Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…

The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to…

Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…

A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…

Modularity is widely used to effectively measure the strength of the disjoint community structure found by community detection algorithms. Several overlapping extensions of modularity were proposed to measure the quality of overlapping…

We characterize the large-sample properties of network modularity in the presence of covariates, under a natural and flexible nonparametric null model. This provides for the first time an objective measure of whether or not a particular…

We improve current instability-based methods for the selection of the number of clusters $k$ in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously…

Traditionally, graph quality metrics focus on readability, but recent studies show the need for metrics which are more specific to the discovery of patterns in graphs. Cluster analysis is a popular task within graph analysis, yet there is…

Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…