Related papers: $K$-Means and Gaussian Mixture Modeling with a Sep…

The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is…

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.…

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…

We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m x n matrices A such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD…

In single-particle cryo-electron microscopy (cryo-EM), K-means clustering algorithm is widely used in unsupervised 2D classification of projection images of biological macromolecules. 3D ab initio reconstruction requires accurate…

We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…

Among all the partition based clustering algorithms K-means is the most popular and well known method. It generally shows impressive results even in considerably large data sets. The computational complexity of K-means does not suffer from…

In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…

We consider the problem of data clustering with unidentified feature quality and when a small amount of labelled data is provided. An unsupervised sparse clustering method can be employed in order to detect the subgroup of features…

$k$-means clustering is NP-hard in the worst case but previous work has shown efficient algorithms assuming the optimal $k$-means clusters are \emph{stable} under additive or multiplicative perturbation of data. This has two caveats. First,…

We present an approach to clustering time series data using a model-based generalization of the K-Means algorithm which we call K-Models. We prove the convergence of this general algorithm and relate it to the hard-EM algorithm for mixture…

While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…

In longitudinal data analysis, observation points of repeated measurements over time often vary among subjects except in well-designed experimental studies. Additionally, measurements for each subject are typically obtained at only a few…

This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

We present a $k$-means-based clustering algorithm, which optimizes the mean square error, for given cluster sizes. A straightforward application is balanced clustering, where the sizes of each cluster are equal. In the $k$-means assignment…

Although extensive research exists in spatial modeling, few studies have addressed finite mixture model-based clustering methods for spatial data. Finite mixture models, especially Gaussian mixture models, particularly suffer from high…

The Gaussian mixture model (GMM) provides a simple yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM),…

We consider the problem of spherical Gaussian Mixture models with $k \geq 3$ components when the components are well separated. A fundamental previous result established that separation of $\Omega(\sqrt{\log k})$ is necessary and sufficient…

The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the…