Related papers: Inapproximability for Local Correlation Clustering…
In the Max-k-diameter problem, we are given a set of points in a metric space, and the goal is to partition the input points into k parts such that the maximum pairwise distance between points in the same part of the partition is minimized.…
In supervised clustering, standard techniques for learning a pairwise dissimilarity function often suffer from a discrepancy between the training and clustering objectives, leading to poor cluster quality. Rectifying this discrepancy…
In this paper, we study parallel algorithms for the correlation clustering problem, where every pair of two different entities is labeled with similar or dissimilar. The goal is to partition the entities into clusters to minimize the number…
Correlation Clustering is a fundamental clustering problem, and there has been a line of work on improving the approximation ratio for this problem in recent years. A key algorithmic component in these works is the cluster LP. Chromatic…
Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs. These objectives are parameterized by one or more resolution parameters in order to…
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…
Clustering is a fundamental unsupervised learning problem where a dataset is partitioned into clusters that consist of nearby points in a metric space. A recent variant, fair clustering, associates a color with each point representing its…
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…
Fast approximate nearest neighbor (NN) search in large databases is becoming popular. Several powerful learning-based formulations have been proposed recently. However, not much attention has been paid to a more fundamental question: how…
Clustering consists of partitioning data objects into subsets called clusters according to some similarity criteria. This paper addresses a generalization called quasi-clustering that allows overlapping of clusters, and which we link to…
Clustering is a fundamental building block of modern statistical analysis pipelines. Fair clustering has seen much attention from the machine learning community in recent years. We are some of the first to study fairness in the context of…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
Contrastive learning is a powerful technique for discovering meaningful data representations by optimizing objectives based on $\textit{contrastive information}$, often given as a set of weighted triplets $\{(x_i, y_i^+, z_{i}^-)\}_{i =…
We show that it is Unique Games-hard to approximate the maximum of a submodular function to within a factor 0.695, and that it is Unique Games-hard to approximate the maximum of a symmetric submodular function to within a factor 0.739.…
Capacitated fair-range $k$-clustering generalizes classical $k$-clustering by incorporating both capacity constraints and demographic fairness. In this setting, each facility has a capacity limit and may belong to one or more demographic…
The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games…
Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set $X$ of $n$ points and two integers $k$ and $m$, the clustering with outliers aims to exclude $m$ points from $X$ and partition the remaining…
The goal of the \emph{alignment problem} is to align a (given) point cloud $P = \{p_1,\cdots,p_n\}$ to another (observed) point cloud $Q = \{q_1,\cdots,q_n\}$. That is, to compute a rotation matrix $R \in \mathbb{R}^{3 \times 3}$ and a…
Several clustering frameworks with interactive (semi-supervised) queries have been studied in the past. Recently, clustering with same-cluster queries has become popular. An algorithm in this setting has access to an oracle with full…
Constraints on the validity of the hierarchical gravitational instability theory and the evolution of biasing are presented based upon measurements of higher order clustering statistics in the Deeprange Survey, a catalog of $\sim710,000$…