Related papers: MAP Clustering under the Gaussian Mixture Model vi…

This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal…

We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…

Plain vanilla K-means clustering has proven to be successful in practice, yet it suffers from outlier sensitivity and may produce highly unbalanced clusters. To mitigate both shortcomings, we formulate a joint outlier detection and…

Gaussian mixture model is very useful in many practical problems. Nevertheless, it cannot be directly generalized to non Euclidean spaces. To overcome this problem we present a spherical Gaussian-based clustering approach for partitioning…

The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data.…

Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e.…

We propose a clustering-based iterative algorithm to solve certain optimization problems in machine learning, where we start the algorithm by aggregating the original data, solving the problem on aggregated data, and then in subsequent…

Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…

Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic model, finding an exact solution for MAP inference is often intractable. Thus, many approximation…

We propose a novel global solution algorithm for the network-constrained unit commitment problem incorporating a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming…

Gaussian Mixture models (GMMs) are a powerful tool for clustering, classification and density estimation when clustering structures are embedded in the data. The presence of missing values can largely impact the GMMs estimation process,…

Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…

In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior…

The two main topics of this paper are the introduction of the "optimally tuned improper maximum likelihood estimator" (OTRIMLE) for robust clustering based on the multivariate Gaussian model for clusters, and a comprehensive simulation…

We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…

We propose a Bayesian approach for model-based clustering of multivariate categorical data where variables are allowed to be associated within clusters and the number of clusters is unknown. The approach uses a two-layer mixture of finite…

Information-maximization clustering learns a probabilistic classifier in an unsupervised manner so that mutual information between feature vectors and cluster assignments is maximized. A notable advantage of this approach is that it only…

We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…

Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…

We present a theoretical analysis of Maximum a Posteriori (MAP) sequence estimation for binary symmetric hidden Markov processes. We reduce the MAP estimation to the energy minimization of an appropriately defined Ising spin model, and…