Related papers: Mean-field theory of Bayesian clustering
In this paper we propose a framework inspired by interacting particle physics and devised to perform clustering on multidimensional datasets. To this end, any given dataset is modeled as an interacting particle system, under the assumption…
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…
A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold…
A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges…
We present a new model-based integrative method for clustering objects given both vectorial data, which describes the feature of each object, and network data, which indicates the similarity of connected objects. The proposed general model…
Spectral clustering views the similarity matrix as a weighted graph, and partitions the data by minimizing a graph-cut loss. Since it minimizes the across-cluster similarity, there is no need to model the distribution within each cluster.…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
Cluster analysis aims at partitioning data into groups or clusters. In applications, it is common to deal with problems where the number of clusters is unknown. Bayesian mixture models employed in such applications usually specify a…
We derive a new Bayesian Information Criterion (BIC) by formulating the problem of estimating the number of clusters in an observed data set as maximization of the posterior probability of the candidate models. Given that some mild…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
Clustering is a technique for the analysis of datasets obtained by empirical studies in several disciplines with a major application for biomedical research. Essentially, clustering algorithms are executed by machines aiming at finding…
In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…
Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is…
We introduce a new clustering method for the classification of functional data sets by their probabilistic law, that is, a procedure that aims to assign data sets to the same cluster if and only if the data were generated with the same…
The paper presents the algorithm for clustering a dataset by grouping the optimal, from the point of view of the BIC criterion, number of Gaussian clusters into the optimal, from the point of view of their statistical separability,…
Identification of the clusters from an unlabeled data set is one of the most important problems in Unsupervised Machine Learning. The state of the art clustering algorithms are based on either the statistical properties or the geometric…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…
A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each…