Related papers: Information theoretical clustering is hard to appr…

A new interpoint distance-based measure is proposed to identify the optimal number of clusters present in a data set. Designed in nonparametric approach, it is independent of the distribution of given data. Interpoint distances between the…

Density matrix embedding theory (Phys. Rev. Lett. 109, 186404 (2012)) and density embedding theory ((Phys. Rev. B 89, 035140 (2014)) have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work,…

We suggest efficient and provable methods to compute an approximation for imbalanced point clustering, that is, fitting $k$-centers to a set of points in $\mathbb{R}^d$, for any $d,k\geq 1$. To this end, we utilize \emph{coresets}, which,…

There is no, nor will there ever be, single best clustering algorithm. Nevertheless, we would still like to be able to distinguish between methods that work well on certain task types and those that systematically underperform. Clustering…

Promoting fairness for deep clustering models in unsupervised clustering settings to reduce demographic bias is a challenging goal. This is because of the limitation of large-scale balanced data with well-annotated labels for sensitive or…

Clustering is an underspecified task: there are no universal criteria for what makes a good clustering. This is especially true for relational data, where similarity can be based on the features of individuals, the relationships between…

Consider a defined density on a set of very large dimension. It is quite difficult to find an estimate of this density from a data set. However, it is possible through a projection pursuit methodology to solve this problem. Touboul's…

Nonhierarchical clustering depending on unsupervised algorithms may not retrieve the optimal partition of datasets. Determining if clusters fit ``natural partitions`` can be achieved using cluster validity indices (CVIs). Most existing CVIs…

Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually…

Given a set of points $P \subset \mathbb{R}^d$, the $k$-means clustering problem is to find a set of $k$ {\em centers} $C = \{c_1,...,c_k\}, c_i \in \mathbb{R}^d,$ such that the objective function $\sum_{x \in P} d(x,C)^2$, where $d(x,C)$…

While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence…

In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…

Whether class labels in a given data set correspond to meaningful clusters is crucial for the evaluation of clustering algorithms using real-world data sets. This property can be quantified by separability measures. The central aspects of…

Entropy measures of probability distributions are widely used measures in ecology, biology, genetics, and in other fields, to quantify species diversity of a community. Unfortunately, entropy-based diversity indices, or diversity indices…

Entanglement in J_1-J_2, S=1/2 quantum spin chains with an impurity is studied using analytic methods as well as large scale numerical density matrix renormalization group methods. The entanglement is investigated in terms of the von…

We introduce a new approach to deciding the number of clusters. The approach is applied to Optimally Tuned Robust Improper Maximum Likelihood Estimation (OTRIMLE; Coretto and Hennig 2016) of a Gaussian mixture model allowing for…

Many cluster similarity indices are used to evaluate clustering algorithms, and choosing the best one for a particular task remains an open problem. We demonstrate that this problem is crucial: there are many disagreements among the…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…

The long disputed issue of the limiting value of quasiparticle density of states $\r(0) = \r (\e \to 0)$ in a \emph{d-}wave superconductor with impurities (\emph{vs} its linear vanishing, $\r_0(\e) \propto |\e|/\D$, near the nodal point $\e…