A True $$O(n\log {n})$$ Algorithm for the All-k-Nearest-Neighbors Problem

Ma, Hengzhao; Li, Jianzhong

doi:10.1007/978-3-030-36412-0_29

Cited by 3 publications

(2 citation statements)

References 32 publications

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“…Further, the cost of computing the low-lying spectrum of the graph Laplacian using iterative methods scales as 40 , 41 . However, both these costs can be reduced by setting a cutoff on the number of edges per node on the graph using, for example, an efficient implementation of the nearest neighbors algorithm 42 . In this case, the cost of the specMF algorithm scales as , where is the cutoff on the maximum number of neighbors for every node.…”

Section: Discussionmentioning

confidence: 99%

Graph Laplacian-based spectral multi-fidelity modeling

Pinti,

Oberai

2023

Sci Rep

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Low-fidelity data is typically inexpensive to generate but inaccurate, whereas high-fidelity data is accurate but expensive. To address this, multi-fidelity methods use a small set of high-fidelity data to enhance the accuracy of a large set of low-fidelity data. In the approach described in this paper, this is accomplished by constructing a graph Laplacian from the low-fidelity data and computing its low-lying spectrum. This is used to cluster the data and identify points closest to the cluster centroids, where high-fidelity data is acquired. Thereafter, a transformation that maps every low-fidelity data point to a multi-fidelity counterpart is determined by minimizing the discrepancy between the multi- and high-fidelity data while preserving the underlying structure of the low-fidelity data distribution. The method is tested with problems in solid and fluid mechanics. By utilizing only a small fraction of high-fidelity data, the accuracy of a large set of low-fidelity data is significantly improved.

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Section: Discussionmentioning

confidence: 99%

Graph Laplacian-based spectral multi-fidelity modeling

Pinti,

Oberai

2023

Sci Rep

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“…For example, k-d tree has average O(log N ) complexity to find the nearest neighbor of a sample in randomly distributed datasets [47]. Moreover, for Euclidean space, it is possible to find k nearest neighbors of every sample in O(k 2 N ) time [48].…”

Section: B Nearest Neighbor Search Methodsmentioning

confidence: 99%

Natural Hierarchical Cluster Analysis by Nearest Neighbors with Near-Linear Time Complexity

Gokcesu¹,

Gokcesu²

2022

Preprint

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We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the iterative working of the algorithm, in the sense that the partitions of the hierarchical clusters are purely defined in accordance with the input dataset. Our method is a universal hierarchical clustering approach since it can be implemented as bottom up or top down versions, both of which result in the same clustering. We show that for certain types of datasets, our algorithm has near-linear time and space complexity.

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