Related papers: Layers and stability
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 derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
We introduce ordered and unordered configuration spaces of 'clusters' of points in an Euclidean space $\mathbb{R}^d$, where points in each cluster satisfy a 'verticality' condition, depending on a decomposition $d=p+q$. We compute the…
Stability selection (Meinshausen and Buhlmann, 2010) makes any feature selection method more stable by returning only those features that are consistently selected across many subsamples. We prove (in what is, to our knowledge, the first…
DBSCAN is a classical density-based clustering procedure with tremendous practical relevance. However, DBSCAN implicitly needs to compute the empirical density for each sample point, leading to a quadratic worst-case time complexity, which…
This paper focuses on density-based clustering, particularly the Density Peak (DP) algorithm and the one based on density-connectivity DBSCAN; and proposes a new method which takes advantage of the individual strengths of these two methods…
Classically, Bayesian clustering interprets each component of a mixture model as a cluster. The inferred clustering posterior is highly sensitive to any inaccuracies in the kernel within each component. As this kernel is made more flexible,…
In this paper we present a new dynamical systems algorithm for clustering in hyperspectral images. The main idea of the algorithm is that data points are \`pushed\' in the direction of increasing density and groups of pixels that end up in…
This paper describes the incremental behaviours of Density based clustering. It specially focuses on the Density Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm and its incremental approach.DBSCAN relies on a density…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
Traditional studies of stellar clusters in external galaxies use surface photometry and therefore focus on systems that are still bright and compact enough to be separated from the stellar background. Consequently, the latter stages of…
Galaxy clusters as gravitational lenses play a unique role in astrophysics and cosmology: they permit mapping the dark matter distribution on a range of scales; they reveal the properties of high and intermediate redshift background…
The baryon fraction of galaxy clusters in numerical simulations is found to be dependant on the cluster formation method. In all cases, the gas is anti-biased compared with the dark matter. However, clusters formed hierarchically are found…
Clusters of galaxies acting as gravitational lenses deform the images of background galaxies. For small galaxies the deformation is determined by the local properties of the lens (shear, convergence). Small circular shaped galaxies are seen…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
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…
Visual scene decomposition into semantic entities is one of the major challenges when creating a reliable object grasping system. Recently, we introduced a bottom-up hierarchical clustering approach which is able to segment objects and…
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…