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We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic…

Data Structures and Algorithms · Computer Science 2007-05-23 David Eppstein

This paper presents a novel framework in which video/image segmentation and localization are cast into a single optimization problem that integrates information from low level appearance cues with that of high level localization cues in a…

Computer Vision and Pattern Recognition · Computer Science 2018-11-27 Abhishek Sharma

We present combinatorial approximation algorithms for the weighted correlation clustering problem. In this problem, we have a set of vertices and two weight values for each pair of vertices, denoting their difference and similarity. The…

Data Structures and Algorithms · Computer Science 2025-07-16 Mojtaba Ostovari , Alireza Zarei

In the Correlation Clustering problem, we are given a weighted graph $G$ with its edges labeled as "similar" or "dissimilar" by a binary classifier. The goal is to produce a clustering that minimizes the weight of "disagreements": the sum…

Data Structures and Algorithms · Computer Science 2021-08-13 Jafar Jafarov , Sanchit Kalhan , Konstantin Makarychev , Yury Makarychev

Visual grouping is a key mechanism in human scene perception. There, it belongs to the subconscious, early processing and is key prerequisite for other high level tasks such as recognition. In this paper, we introduce an efficient, realtime…

Computer Vision and Pattern Recognition · Computer Science 2016-09-23 Dominik Alexander Klein , Dirk Schulz , Armin Bernd Cremers

How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view.…

Social and Information Networks · Computer Science 2016-06-06 Junming Shao , Qinli Yang , Jinhu Liu , Stefan Kramer

Correlation clustering seeks a partition of the vertex set of a given graph/network into groups of closely related, or just close enough, vertices so that elements of different groups are not close to each other. The problem has been…

Social and Information Networks · Computer Science 2024-12-05 Faisal N. Abu-Khzam , Lucas Isenmann , Sergio Thoumi

Constructing a similarity graph from a set $X$ of data points in $\mathbb{R}^d$ is the first step of many modern clustering algorithms. However, typical constructions of a similarity graph have high time complexity, and a quadratic space…

Data Structures and Algorithms · Computer Science 2023-10-24 Peter Macgregor , He Sun

Superpixel segmentation consists of partitioning images into regions composed of similar and connected pixels. Its methods have been widely used in many computer vision applications since it allows for reducing the workload, removing…

Computer Vision and Pattern Recognition · Computer Science 2024-10-01 I. B. Barcelos , F. de C. Belém , L. de M. João , Z. K. G. do Patrocínio , A. X. Falcão , S. J. F. Guimarães

Properly estimating correlations between objects at different spatial scales necessitates $\mathcal{O}(n^2)$ distance calculations. For this reason, most widely adopted packages for estimating correlations use clustering algorithms to…

We propose a novel approach for optimizing the graph ratio-cut by modeling the binary assignments as random variables. We provide an upper bound on the expected ratio-cut, as well as an unbiased estimate of its gradient, to learn the…

Machine Learning · Computer Science 2025-03-12 Ayoub Ghriss , Claire Monteleoni

We present an efficient and robust approach for extracting clusters of galaxies from weak lensing survey data and measuring their properties. We use simple, physically-motivated cluster models appropriate for such sparse, noisy data, and…

Astrophysics · Physics 2008-10-07 F. Feroz , P. J. Marshall , M. P. Hobson

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…

Data Structures and Algorithms · Computer Science 2019-08-15 Barna Saha , Sanjay Subramanian

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…

Computational Geometry · Computer Science 2018-09-11 Hu Ding

In this paper, we present an approach to search result clustering, using partitioning of underlying link graph. We define the notion of "query-induced subgraph" and formulate the problem of search result clustering as a problem of efficient…

Information Retrieval · Computer Science 2008-11-27 Aleksandar Bradic

We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…

Machine Learning · Statistics 2014-11-03 Dohyung Park , Constantine Caramanis , Sujay Sanghavi

Many image segmentation techniques have been developed over the past two decades for segmenting the images, which help for object recognition, occlusion boundary estimation within motion or stereo systems, image compression, image editing.…

Computer Vision and Pattern Recognition · Computer Science 2014-06-03 Shradha Dakhare , Harshal Chowhan , Manoj B. Chandak

As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that…

Optimization and Control · Mathematics 2019-02-18 Aleksis Pirinen , Brendan Ames

In the face of complex natural images, existing deep clustering algorithms fall significantly short in terms of clustering accuracy when compared to supervised classification methods, making them less practical. This paper introduces an…

Machine Learning · Computer Science 2024-08-13 Qiuyu Zhu , Liheng Hu , Sijin Wang

Clustering graphs based on a comparison of the number of links within clusters and the expected value of this quantity in a random graph has gained a lot of attention and popularity in the last decade. Recently, Aldecoa and Marin proposed a…

Data Structures and Algorithms · Computer Science 2013-10-23 Tobias Fleck , Andrea Kappes , Dorothea Wagner