Related papers: Subspace Clustering using Ensembles of $K$-Subspac…

$K$-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…

In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of…

Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…

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…

Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…

This paper focuses on the sparse subspace clustering problem, and develops an online algorithmic solution to cluster data points on-the-fly, without revisiting the whole dataset. The strategy involves an online solution of a sparse…

The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…

A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different…

Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in…

Subspace clustering is a growing field of unsupervised learning that has gained much popularity in the computer vision community. Applications can be found in areas such as motion segmentation and face clustering. It assumes that data…

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…

We present a unified framework that yields EPASes for constrained $(k,z)$-clustering in metric spaces of bounded (algorithmic) scatter dimension, a notion introduced by Abbasi et al. (FOCS 2023). They showed that several well known metric…

We give the first outlier-robust efficient algorithm for clustering a mixture of $k$ statistically separated d-dimensional Gaussians (k-GMMs). Concretely, our algorithm takes input an $\epsilon$-corrupted sample from a $k$-GMM and whp in…

A simple model to study subspace clustering is the high-dimensional $k$-Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction…

Clustering is a fundamental problem in many areas, which aims to partition a given data set into groups based on some distance measure, such that the data points in the same group are similar while that in different groups are dissimilar.…

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…

Sparse subspace clustering (SSC) is one of the current state-of-the-art methods for partitioning data points into the union of subspaces, with strong theoretical guarantees. However, it is not practical for large data sets as it requires…

Subspace clustering is the classical problem of clustering a collection of data samples that approximately lie around several low-dimensional subspaces. The current state-of-the-art approaches for this problem are based on the…

Deep subspace clustering networks have attracted much attention in subspace clustering, in which an auto-encoder non-linearly maps the input data into a latent space, and a fully connected layer named self-expressiveness module is…

This article details the algorithmics in FLSSS, an R package for solving various subset sum problems. The fundamental algorithm engages the problem via combinatorial space compression adaptive to constraints, relaxations and variations that…