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We present a general methodology that learns to classify images without labels by leveraging pretrained feature extractors. Our approach involves self-distillation training of clustering heads based on the fact that nearest neighbours in…

Despite its well-known shortcomings, $k$-means remains one of the most widely used approaches to data clustering. Current research continues to tackle its flaws while attempting to preserve its simplicity. Recently, the \textit{power…

Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…

Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario,…

This work studies the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions on the model, such as moment…

With the recent growth in data availability and complexity, and the associated outburst of elaborate modelling approaches, model selection tools have become a lifeline, providing objective criteria to deal with this increasingly challenging…

A novel family of twelve mixture models with random covariates, nested in the linear $t$ cluster-weighted model (CWM), is introduced for model-based clustering. The linear $t$ CWM was recently presented as a robust alternative to the better…

Fuzzy clustering methods identify naturally occurring clusters in a dataset, where the extent to which different clusters are overlapped can differ. Most methods have a parameter to fix the level of fuzziness. However, the appropriate level…

Ensemble clustering has demonstrated great success in practice; however, its theoretical foundations remain underexplored. This paper examines the generalization performance of ensemble clustering, focusing on generalization error, excess…

One iteration of standard $k$-means (i.e., Lloyd's algorithm) or standard EM for Gaussian mixture models (GMMs) scales linearly with the number of clusters $C$, data points $N$, and data dimensionality $D$. In this study, we explore whether…

Clustering has become an indispensable tool in the presence of increasingly large and complex data sets. Most clustering algorithms depend, either explicitly or implicitly, on the sampled density. However, estimated densities are fragile…

The probability distribution of the magnitude can be modeled by an exponential distribution according to the Gutenberg-Richter relation. Two alternatives are the truncated exponential distribution (TED) and the cut-off exponential…

There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…

We develop a new family of convex relaxations for $k$-means clustering based on sum-of-squares norms, a relaxation of the injective tensor norm that is efficiently computable using the Sum-of-Squares algorithm. We give an algorithm based on…

Variational autoencoder (VAE) and generative adversarial networks (GAN) have found widespread applications in clustering and have achieved significant success. However, the potential of these approaches may be limited due to VAE's mediocre…

The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…

Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen…

We develop a general method for estimating a finite mixture of non-normalized models. Here, a non-normalized model is defined to be a parametric distribution with an intractable normalization constant. Existing methods for estimating…

The mixture model is undoubtedly one of the greatest contributions to clustering. For continuous data, Gaussian models are often used and the Expectation-Maximization (EM) algorithm is particularly suitable for estimating parameters from…

Clustering algorithms start with a fixed divergence, which captures the possibly asymmetric distance between a sample and a centroid. In the mixture model setting, the sample distribution plays the same role. When all attributes have the…