Related papers: A unified framework for hard and soft clustering w…
Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. A common method for fitting finite mixture models is to employ spectral clustering, which…
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…
We develop a new methodology for model-based clustering. Optimizing the log-likelihood provides a principled statistical framework for clustering, with solutions found via the EM algorithm. However, because the log-likelihood is nonconvex,…
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…
The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…
In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy…
Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful…
Any clustering algorithm must synchronously learn to model the clusters and allocate data to those clusters in the absence of labels. Mixture model-based methods model clusters with pre-defined statistical distributions and allocate data to…
We study Sinkhorn EM (sEM), a variant of the expectation maximization (EM) algorithm for mixtures based on entropic optimal transport. sEM differs from the classic EM algorithm in the way responsibilities are computed during the expectation…
Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical…
Extreme learning machine (ELM) is a network model that arbitrarily initializes the first hidden layer and can be computed speedily. In order to improve the classification performance of ELM, a $\ell_2$ and $\ell_{0.5}$ regularization ELM…
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…
Research on cluster analysis for categorical data continues to develop, with new clustering algorithms being proposed. However, in this context, the determination of the number of clusters is rarely addressed. In this paper, we propose a…
We study inference in stochastic block models (SBMs) through the lens of optimal transport (OT). We first establish that maximum likelihood variational inference (MLVI) can be interpreted as a semi-relaxed Gromov-Wasserstein (srGW)…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…
With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering…
In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…
Clustering high-dimensional data is especially challenging when cluster distributions are heavy tailed and only approximately elliptical. Existing high-dimensional methods are largely built for Gaussian or other light-tailed models, whereas…