相关论文: Correlation Clustering with Sherali-Adams

We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and…

Introducing an active space approximation is inevitable for the quantum computations of chemical systems. However, this approximation ignores the electron correlations related to non-active orbitals. Here, we propose a computational method…

We study the problem of applying spectral clustering to cluster multi-scale data, which is data whose clusters are of various sizes and densities. Traditional spectral clustering techniques discover clusters by processing a similarity…

The multiway-cut problem is, given a weighted graph and k >= 2 terminal nodes, to find a minimum-weight set of edges whose removal separates all the terminals. The problem is NP-hard, and even NP-hard to approximate within 1+delta for some…

Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges. The prevailing clustering algorithms widely depend on…

We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the…

We show that for constraint satisfaction problems (CSPs), sub-exponential size linear programming relaxations are as powerful as $n^{\Omega(1)}$-rounds of the Sherali-Adams linear programming hierarchy. As a corollary, we obtain…

In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\eps$-coreset for this problem is a weighted (scaled)…

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…

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…

Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…

We study coresets for clustering with capacity and fairness constraints. Our main result is a near-linear time algorithm to construct $\tilde{O}(k^2\varepsilon^{-2z-2})$-sized $\varepsilon$-coresets for capacitated $(k,z)$-clustering which…

We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form…

Metric facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. The capacity-constrained generalizations, such as capacitated facility location…

Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are…

Hierarchical clustering remains a fundamental challenge in data mining, particularly when dealing with large-scale datasets where traditional approaches fail to scale effectively. Recent Chameleon-based algorithms - Chameleon2, M-Chameleon,…

The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…

In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon…

This work aims to improve the sample efficiency of parallel large-scale ranking and selection (R&S) problems by leveraging correlation information. We modify the commonly used "divide and conquer" framework in parallel computing by adding a…