Related papers: Information theoretical clustering is hard to appr…
We consider a clustering problem where we observe feature vectors $X_i \in R^p$, $i = 1, 2, \ldots, n$, from $K$ possible classes. The class labels are unknown and the main interest is to estimate them. We are primarily interested in the…
Data Science and Machine Learning have become fundamental assets for companies and research institutions alike. As one of its fields, supervised classification allows for class prediction of new samples, learning from given training data.…
VARCLUST algorithm is proposed for clustering variables under the assumption that variables in a given cluster are linear combinations of a small number of hidden latent variables, corrupted by the random noise. The entire clustering task…
We consider inapproximability of the correlation clustering problem defined as follows: Given a graph $G = (V,E)$ where each edge is labeled either "+" (similar) or "-" (dissimilar), correlation clustering seeks to partition the vertices…
We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based…
In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace…
Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem…
Consider a population consisting of clusters of sampling units, evolving temporally, spatially, or according to other dynamics. We wish to monitor the evolution of its means, medians, or other parameters. For administrative convenience and…
\textit{Clustering problems} often arise in the fields like data mining, machine learning etc. to group a collection of objects into similar groups with respect to a similarity (or dissimilarity) measure. Among the clustering problems,…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
Describing a quantum impurity coupled to one or more non-interacting fermionic reservoirs is a paradigmatic problem in quantum many-body physics. While historically the focus has been on the equilibrium properties of the impurity-reservoir…
We study the large sample behavior of a convex clustering framework, which minimizes the sample within cluster sum of squares under an~$\ell_1$ fusion constraint on the cluster centroids. This recently proposed approach has been gaining in…
In this contribution, the clustering procedure based on K-Means algorithm is studied as an inverse problem, which is a special case of the illposed problems. The attempts to improve the quality of the clustering inverse problem drive to…
We construct a cross-entropy clustering (CEC) theory which finds the optimal number of clusters by automatically removing groups which carry no information. Moreover, our theory gives simple and efficient criterion to verify cluster…
This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…
Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented…
We present a mapping of correlated multi-impurity Anderson models to a cluster model coupled to a number of effective conduction bands capturing its essential low-energy physics. The major ingredient is the complex single-particle self…
In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that…
We establish Multilayer Correlation Clustering, a novel generalization of Correlation Clustering to the multilayer setting. In this model, we are given a series of inputs of Correlation Clustering (called layers) over the common set $V$ of…