Related papers: Mean field models for large data-clustering proble…

We introduce the functional mean-shift algorithm, an iterative algorithm for estimating the local modes of a surrogate density from functional data. We show that the algorithm can be used for cluster analysis of functional data. We propose…

The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are…

Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density.…

A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…

Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering…

Quality assessments of models in unsupervised learning and clustering verification in particular have been a long-standing problem in the machine learning research. The lack of robust and universally applicable cluster validity scores often…

We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…

A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…

This article proposes a mixture modeling approach to estimating cluster-wise conditional distributions in clustered (grouped) data. We adapt the mixture-of-experts model to the latent distributions, and propose a model in which each…

In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo…

Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an…

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…

Clustering is a powerful and extensively used data science tool. While clustering is generally thought of as an unsupervised learning technique, there are also supervised variations such as Spath's clusterwise regression that attempt to…

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 work, we formulate an abstract framework to study mean-field systems. In contrast to most approaches in the available literature which primarily rely on the analysis of SDEs, ours is based on optimal transport and semigroup theory.…

Clustered data is ubiquitous in a variety of scientific fields. In this paper, we propose a flexible and interpretable modeling approach, called grouped heterogenous mixture modeling, for clustered data, which models cluster-wise…

This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…

We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a wide-range of equilibrium systems. Anomalous…

Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…