Related papers: Splitting Methods for Convex Clustering
This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a…
We propose a new relative-error inexact version of the alternating direction method of multipliers (ADMM) for convex optimization. We prove the asymptotic convergence of our main algorithm as well as pointwise and ergodic…
Although the field of distributed optimization is well-developed, relevant literature focused on the application of distributed optimization to multi-robot problems is limited. This survey constitutes the second part of a two-part series on…
We present a study on how to effectively reduce the dimensions of the $k$-means clustering problem, so that provably accurate approximations are obtained. Four algorithms are presented, two \textit{feature selection} and two \textit{feature…
This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In…
Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC…
This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…
Several methods have been recently proposed for estimating sparse Gaussian graphical models using $\ell_{1}$ regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even…
The anticlustering problem is to partition a set of objects into K equal-sized anticlusters such that the sum of distances within anticlusters is maximized. The anticlustering problem is NP-hard. We focus on anticlustering in Euclidean…
The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these…
We tackle highly nonconvex, nonsmooth composite optimization problems whose objectives comprise a Moreau-Yosida regularized term. Classical nonconvex proximal splitting algorithms, such as nonconvex ADMM, suffer from lack of convergence for…
Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…
Recently, heuristics based on the Douglas-Rachford splitting algorithm and the alternating direction method of multipliers (ADMM) have found empirical success in minimizing convex functions over nonconvex sets, but not much has been done to…
Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…
This note serves two purposes. Firstly, we construct a counterexample to show that the statement on the convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex optimization problems in a…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
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…
Biclustering is the task of simultaneously clustering the rows and columns of the data matrix into different subgroups such that the rows and columns within a subgroup exhibit similar patterns. In this paper, we consider the case of…
Spectral Clustering (SC) is one of the most widely used methods for data clustering. It first finds a low-dimensonal embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on…