Related papers: Scalable Laplacian K-modes
We address the problem of validating the ouput of clustering algorithms. Given data $\mathcal{D}$ and a partition $\mathcal{C}$ of these data into $K$ clusters, when can we say that the clusters obtained are correct or meaningful for the…
Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about…
We design new differentially private algorithms for the Euclidean k-means problem, both in the centralized model and in the local model of differential privacy. In both models, our algorithms achieve significantly improved error guarantees…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
In this paper, we provide non-asymptotic upper bounds on the error of sampling from a target density using three schemes of discretized Langevin diffusions. The first scheme is the Langevin Monte Carlo (LMC) algorithm, the Euler…
Many algorithms for approximate nearest neighbor search in high-dimensional spaces partition the data into clusters. At query time, in order to avoid exhaustive search, an index selects the few (or a single) clusters nearest to the query…
In discrete k-center and k-median clustering, we are given a set of points P in a metric space M, and the task is to output a set C \subseteq ? P, |C| = k, such that the cost of clustering P using C is as small as possible. For k-center,…
VARCLUST algorithm is proposed for clustering variables under the assumption that variables in a given cluster are linear combinations of a small number of hidden latent variables, corrupted by the random noise. The entire clustering task…
Minimax problems have recently attracted a lot of research interests. A few efforts have been made to solve decentralized nonconvex strongly-concave (NCSC) minimax-structured optimization; however, all of them focus on smooth problems with…
This paper considers a class of distributed resource allocation problems where each agent privately holds a smooth, potentially non-convex local objective, subject to a globally coupled equality constraint. Built upon the existing method,…
Over the last three decades, researchers have intensively explored various clustering tools for categorical data analysis. Despite the proposal of various clustering algorithms, the classical k-modes algorithm remains a popular choice for…
Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…
We consider the problem of clustering in the presence of noise. That is, when on top of cluster structure, the data also contains a subset of \emph{unstructured} points. Our goal is to detect the clusters despite the presence of many…
A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…
We propose a new variant of the k-median problem, where the objective function models not only the cost of assigning data points to cluster representatives, but also a penalty term for disagreement among the representatives. We motivate…
We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…