Relative neighborhood graphs and their relatives

Jaromczyk, Jerzy W.; Toussaint, Godfried T.

doi:10.1109/5.163414

Cited by 528 publications

(358 citation statements)

References 83 publications

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“…This notion is an extension of the notion of proximity graph as explained in the survey article [17]; see also [20] and the literature on topology control in wireless networks for related references.…”

Section: Proximity Graphsmentioning

confidence: 99%

Spatially-distributed coverage optimization and control with limited-range interactions

2005

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Abstract. This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.Mathematics Subject Classification. 37N35, 49J52, 68W15, 93D20.

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Section: Proximity Graphsmentioning

confidence: 99%

Spatially-distributed coverage optimization and control with limited-range interactions

2005

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“…However, this lexicon must be comprehensive enough to ensure discrimination from a graph from another. They have therefore decided to take as a baseline the non-isomorphic graphs network presented in [9]. The network presents all graphs composed of n edges up to N (where N is the maximum number of edges).…”

Section: Methods 1: Topological Embeddingmentioning

confidence: 99%

A Comparison of Explicit and Implicit Graph Embedding Methods for Pattern Recognition

Conte

Ramel

Sidère

et al. 2013

Graph-Based Representations in Pattern Recognition

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Abstract. In recent years graph embedding has emerged as a promising solution for enabling the expressive, convenient, powerful but computational expensive graph based representations to benefit from mature, less expensive and efficient state of the art machine learning models of statistical pattern recognition. In this paper we present a comparison of two implicit and three explicit state of the art graph embedding methodologies. Our preliminary experimentation on different chemoinformatics datasets illustrates that the two implicit and three explicit graph embedding approaches obtain competitive performance for the problem of graph classification.

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“…The NCN Editing (NCNE) approach corresponds to slight modification of the original work of Wilson and basically consists of using the error estimated by the k-NCN classification rule. Proximity graph editing scheme is based on the concepts of Gabriel Graph (GG) and Relative Neighborhood Graph (RNG) [18]. The method applies Wilson's editing algorithm [15] using proximity graphs (GG or RNG) for each sample instead of the Euclidean distance.…”

Section: Wilson Editing Wilsonmentioning

confidence: 99%

Back Propagation with Balanced MSE Cost Function and Nearest Neighbor Editing for Handling Class Overlap and Class Imbalance

Alejo¹,

Sotoca

García

et al. 2011

Lecture Notes in Computer Science

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Abstract. The class imbalance problem has been considered a critical factor for designing and constructing the supervised classifiers. In the case of artificial neural networks, this complexity negatively affects the generalization process on under-represented classes. However, it has also been observed that the decrease in the performance attainable of standard learners is not directly caused by the class imbalance, but is also related with other difficulties, such as overlapping. In this work, a new empirical study for handling class overlap and class imbalance on multi-class problem is described. In order to solve this problem, we propose the joint use of editing techniques and a modified MSE cost function for MLP. This analysis was made on a remote sensing data . The experimental results demonstrate the consistency and validity of the combined strategy here proposed.

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Relative neighborhood graphs and their relatives

Cited by 528 publications

References 83 publications

Spatially-distributed coverage optimization and control with limited-range interactions

Spatially-distributed coverage optimization and control with limited-range interactions

A Comparison of Explicit and Implicit Graph Embedding Methods for Pattern Recognition

Back Propagation with Balanced MSE Cost Function and Nearest Neighbor Editing for Handling Class Overlap and Class Imbalance

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