Related papers: Constant Approximation for Individual Preference S…

We study the robustness--the invariance under definition changes--of the cluster class CL#P [HHKW05]. This class contains each #P function that is computed by a balanced Turing machine whose accepting paths always form a cluster with…

We investigate the unsupervised node classification problem on random hypergraphs under the non-uniform Hypergraph Stochastic Block Model (HSBM) with two equal-sized communities. In this model, edges appear independently with probabilities…

Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A…

We study the notion of perturbation resilience introduced by Bilu and Linial (2010) and Awasthi, Blum, and Sheffet (2012). A clustering problem is $\alpha$-perturbation resilient if the optimal clustering does not change when we perturb all…

There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high-dimensionality of the data, high codimension in the ambient space of the data manifolds of interest, and…

We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based…

There are growing concerns that algorithms, which increasingly make or influence important decisions pertaining to individuals, might produce outcomes that discriminate against protected groups. We study such fairness concerns in the…

Graph clustering becomes an important problem due to emerging applications involving the web, social networks and bio-informatics. Recently, many such applications generate data in the form of streams. Clustering massive, dynamic graph…

Despite the widespread use of Clustering, there is distressingly little general theory of clustering available. Questions like "What distinguishes a clustering of data from other data partitioning?", "Are there any principles governing all…

In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…

A clustering is an implicit assignment of labels of points, based on proximity to other points. It is these labels that are then used for downstream analysis (either focusing on individual clusters, or identifying representatives of…

Clustering is a foundational problem in machine learning with numerous applications. As machine learning increases in ubiquity as a backend for automated systems, concerns about fairness arise. Much of the current literature on fairness…

Crowdsourced, or human computation based clustering algorithms usually rely on relative distance comparisons, as these are easier to elicit from human workers than absolute distance information. A relative distance comparison is a statement…

Clustering is considered a non-supervised learning setting, in which the goal is to partition a collection of data points into disjoint clusters. Often a bound $k$ on the number of clusters is given or assumed by the practitioner. Many…

We construct a framework for studying clustering algorithms, which includes two key ideas: persistence and functoriality. The first encodes the idea that the output of a clustering scheme should carry a multiresolution structure, the second…

Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of…

Numerous papers ask how difficult it is to cluster data. We suggest that the more relevant and interesting question is how difficult it is to cluster data sets {\em that can be clustered well}. More generally, despite the ubiquity and the…

Combinatorial optimization problems for clustering are known to be NP-hard. Most optimization methods are not able to find the global optimum solution for all datasets. To solve this problem, we propose a global optimal path-based…

Correlation clustering is a well-studied problem, first proposed by Bansal, Blum, and Chawla [Mach. Learn. '04]. The input is an unweighted, undirected graph. The problem is to cluster the vertices so as to minimize the number of edges…

We present a new clustering method in the form of a single clustering equation that is able to directly discover groupings in the data. The main proposition is that the first neighbor of each sample is all one needs to discover large chains…