Related papers: PECOK: a convex optimization approach to variable …

Clustering is a fundamental problem in many scientific applications. Standard methods such as $k$-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal.…

We investigate the problem of exact cluster recovery using oracle queries. Previous results show that clusters in Euclidean spaces that are convex and separated with a margin can be reconstructed exactly using only $O(\log n)$ same-cluster…

$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…

Clustering is a usual unsupervised machine learning technique for grouping the data points into groups based upon similar features. We focus here on unsupervised clustering for contaminated data, i.e in the case where K-medians should be…

Recently, Bandeira [arXiv:1509.00824] introduced a new type of algorithm (the so-called probably certifiably correct algorithm) that combines fast solvers with the optimality certificates provided by convex relaxations. In this paper, we…

In this study, we examine a clustering problem in which the covariates of each individual element in a dataset are associated with an uncertainty specific to that element. More specifically, we consider a clustering approach in which a…

The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some…

Convex clustering refers, for given $\left\{x_1, \dots, x_n\right\} \subset \mathbb{R}^p$, to the minimization of \begin{eqnarray*} u(\gamma) & = & \underset{u_1, \dots, u_n }{\arg\min}\;\sum_{i=1}^{n}{\lVert x_i - u_i \rVert^2} + \gamma…

One iteration of standard $k$-means (i.e., Lloyd's algorithm) or standard EM for Gaussian mixture models (GMMs) scales linearly with the number of clusters $C$, data points $N$, and data dimensionality $D$. In this study, we explore whether…

Identifying clusters of similar objects in data plays a significant role in a wide range of applications. As a model problem for clustering, we consider the densest k-disjoint-clique problem, whose goal is to identify the collection of k…

Here, we propose a clustering technique for general clustering problems including those that have non-convex clusters. For a given desired number of clusters $K$, we use three stages to find a clustering. The first stage uses a hybrid…

In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from…

The fairness of clustering algorithms has gained widespread attention across various areas, including machine learning, In this paper, we study fair $k$-means clustering in Euclidean space. Given a dataset comprising several groups, the…

In the standard planar $k$-center clustering problem, one is given a set $P$ of $n$ points in the plane, and the goal is to select $k$ center points, so as to minimize the maximum distance over points in $P$ to their nearest center. Here we…

We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point.…

We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…

Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…

We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…

We propose an approach to directly estimate the moments or marginals for a high-dimensional equilibrium distribution in statistical mechanics, via solving the high-dimensional Fokker-Planck equation in terms of low-order cluster moments or…

We propose k^2-means, a new clustering method which efficiently copes with large numbers of clusters and achieves low energy solutions. k^2-means builds upon the standard k-means (Lloyd's algorithm) and combines a new strategy to accelerate…