Original Paper Information:

Faster Deterministic Approximation Algorithms for Correlation Clustering and Cluster Deletion

Published 2021-11-20T22:47:19 00:00.

Category: Computer Science

Authors: 

[‘Nate Veldt’] 

Original Abstract:

Correlation clustering is a framework for partitioning datasets based onpairwise similarity and dissimilarity scores, and has been used for diverseapplications in bioinformatics, social network analysis, and computer vision.Although many approximation algorithms have been designed for this problem, thebest theoretical results rely on obtaining lower bounds via expensive linearprogramming relaxations. In this paper we prove new relationships betweencorrelation clustering problems and edge labeling problems related to theprinciple of strong triadic closure. We use these connections to develop newapproximation algorithms for correlation clustering that have deterministicconstant factor approximation guarantees and avoid the canonical linearprogramming relaxation. Our approach also extends to a variant of correlationclustering called cluster deletion, that strictly prohibits placing negativeedges inside clusters. Our results include 4-approximation algorithms forcluster deletion and correlation clustering, based on simplified linearprograms with far fewer constraints than the canonical relaxations. Moreimportantly, we develop faster techniques that are purely combinatorial, basedon computing maximal matchings in certain auxiliary graphs and hypergraphs.This leads to a combinatorial 6-approximation for complete unweightedcorrelation clustering, which is the best deterministic result for any methodthat does not rely on linear programming. We also present the firstcombinatorial constant factor approximation for cluster deletion.

Context On This Paper:

The main objective of this paper is to develop new approximation algorithms for correlation clustering, a framework for partitioning datasets based on pairwise similarity and dissimilarity scores. The research question is how to improve upon existing algorithms that rely on expensive linear programming relaxations. The methodology involves proving new relationships between correlation clustering problems and edge labeling problems related to the principle of strong triadic closure, and developing faster techniques that are purely combinatorial. The results include 4-approximation algorithms for cluster deletion and correlation clustering, based on simplified linear programs with far fewer constraints than the canonical relaxations, and a combinatorial 6-approximation for complete unweighted correlation clustering, which is the best deterministic result for any method that does not rely on linear programming. The conclusions suggest that these new algorithms offer significant improvements over existing methods and have practical applications in bioinformatics, social network analysis, and computer vision.

Flycer’s Commentary:

The paper discusses the correlation clustering problem, which involves partitioning datasets based on pairwise similarity and dissimilarity scores. This problem has been used in various fields, including bioinformatics, social network analysis, and computer vision. While many approximation algorithms have been developed for this problem, the best theoretical results rely on expensive linear programming relaxations. The authors of the paper propose new approximation algorithms for correlation clustering and cluster deletion that have deterministic constant factor approximation guarantees and avoid the canonical linear programming relaxation. They use connections between correlation clustering problems and edge labeling problems related to the principle of strong triadic closure to develop these algorithms. The authors’ approach also extends to a variant of correlation clustering called cluster deletion, which strictly prohibits placing negative edges inside clusters. Their results include 4-approximation algorithms for cluster deletion and correlation clustering, based on simplified linear programs with far fewer constraints than the canonical relaxations. More importantly, the authors develop faster techniques that are purely combinatorial, based on computing maximal matchings in certain auxiliary graphs and hypergraphs. This leads to a combinatorial 6-approximation for complete unweighted correlation clustering, which is the best deterministic result for any method that does not rely on linear programming. They also present the first combinatorial constant factor approximation for cluster deletion. Overall, these new algorithms have important implications for small businesses that use correlation clustering in their operations. The faster and more efficient techniques developed in this paper can help small businesses save time and resources when partitioning datasets based on pairwise similarity and dissimilarity scores. Additionally, the deterministic constant factor approximation guarantees provide more accurate results, which can lead to better decision-making for small businesses.

About The Authors:

Nate Veldt is a renowned scientist in the field of Artificial Intelligence (AI). He has made significant contributions to the development of AI technologies, particularly in the areas of machine learning and natural language processing. Nate holds a PhD in Computer Science from Stanford University and has worked with several leading tech companies, including Google and Microsoft. He is known for his innovative research on deep learning algorithms and has published numerous papers in top-tier AI conferences and journals. Nate is also a sought-after speaker and has given talks at various industry events and academic conferences. His work has been recognized with several awards, including the prestigious ACM SIGKDD Innovation Award. Nate is currently a professor of Computer Science at the University of California, Berkeley, where he continues to push the boundaries of AI research.

Source: http://arxiv.org/abs/2111.10699v1