Related papers: PECOK: a convex optimization approach to variable …
In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…
We study the cluster recovery problem in the semi-supervised active clustering framework. Given a finite set of input points, and an oracle revealing whether any two points lie in the same cluster, our goal is to recover all clusters…
We study the optimization landscape of a smooth nonconvex program arising from synchronization over the two-element group $\mathbf{Z}_2$, that is, recovering $z_1, \dots, z_n \in \{\pm 1\}$ from (noisy) relative measurements $R_{ij} \approx…
We study the large sample behavior of a convex clustering framework, which minimizes the sample within cluster sum of squares under an~$\ell_1$ fusion constraint on the cluster centroids. This recently proposed approach has been gaining in…
Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the…
K-means clustering is a cornerstone of data mining, but its efficiency deteriorates when confronted with massive datasets. To address this limitation, we propose a novel heuristic algorithm that leverages the Variable Neighborhood Search…
We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
In industrial resource allocation problems, an initial planning stage may solve a nominal problem instance and a subsequent recovery stage may intervene to repair inefficiencies and infeasibilities due to uncertainty, e.g.\ machine failures…
Segmentation of a colour image composed of different kinds of texture regions can be a hard problem, namely to compute for an exact texture fields and a decision of the optimum number of segmentation areas in an image when it contains…
Ashtiani et al. (NIPS 2016) introduced a semi-supervised framework for clustering (SSAC) where a learner is allowed to make same-cluster queries. More specifically, in their model, there is a query oracle that answers queries of the form…
Although many convex relaxations of clustering have been proposed in the past decade, current formulations remain restricted to spherical Gaussian or discriminative models and are susceptible to imbalanced clusters. To address these…
Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex…
This paper deals with the clustering of univariate observations: given a set of observations coming from $K$ possible clusters, one has to estimate the cluster means. We propose an algorithm based on the minimization of the "KP" criterion…
Clustering is a widely used and powerful machine learning technique, but its effectiveness is often limited by the need to specify the number of clusters, k, or by relying on thresholds that implicitly determine k. We introduce k*-means, a…
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…
We introduce prox-convex for minimizing $F(x)=g(x)+h(C(x))+s(R(x))$, where $g$ and $h$ are convex, $C$ and $s$ are smooth, and each component of $R$ is convex (possibly nonsmooth). Here $g$ captures general convex objectives and indicator…
Clustering mixed-type data, that is, observation by variable data that consist of both continuous and categorical variables poses novel challenges. Foremost among these challenges is the choice of the most appropriate clustering method for…
Identifying a set of homogeneous clusters in a heterogeneous dataset is one of the most important classes of problems in statistical modeling. In the realm of unsupervised partitional clustering, k-means is a very important algorithm for…
Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are…