K-bMOM: A robust Lloyd-type clustering algorithm based on bootstrap median-of-means

Brunet-Saumard, Camille; Genetay, Edouard; Saumard, Adrien

doi:10.1016/j.csda.2021.107370

Cited by 12 publications

(11 citation statements)

References 21 publications

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“…Ye et al, [16] proposed an improved clustering analysis algorithm based on the construction of shape features and peak features of UAV frequency hopping signal waveforms and compared it with K-means, K-means++, DBSCAN, multi-hop and autocorrelation methods [16]. Brunet-Saumard et al, [17] proposed a method called "bootstrap median mean" and designed a clustering algorithm called K-bMOM considering the estimation of the mean of random variables. clustering algorithm called K-bMOM [17].…”

Section: Related Workmentioning

confidence: 99%

“…Brunet-Saumard et al, [17] proposed a method called "bootstrap median mean" and designed a clustering algorithm called K-bMOM considering the estimation of the mean of random variables. clustering algorithm called K-bMOM [17]. The results showed that this algorithm obtained good color quantization performance on simulated and real data sets.…”

Section: Related Workmentioning

confidence: 99%

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Analysis and Application Research of E-Commerce Financial Management Based on T-DPC Optimization Algorithm

Wang,

Shan

2024

Decis. Mak. Appl. Manag. Eng.

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Given the intricate, multifaceted nature of financial data in e-commerce enterprises, this article presents a T-DPC algorithm for analyzing financial management in these businesses. The algorithm utilizes the t-SNE method to reduce the dimensionality of financial data, whilst also implementing an enhanced DPC algorithm based on the K-nearest neighbor concept to analyze financial data clusters. The results show that the F-measure metrics of the DPC algorithm optimized by t-SNE improve 16.7% and 3.07% over the DPC algorithm after testing on the PID and Wine datasets, and its running time is faster than the DPC algorithm on the Aggregation, D31, and R15 datasets by 16.2. Therefore, the algorithm has reference significance for the financial analysis of e-commerce enterprises.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Analysis and Application Research of E-Commerce Financial Management Based on T-DPC Optimization Algorithm

Wang,

Shan

2024

Decis. Mak. Appl. Manag. Eng.

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“…A practical protocol for K-means clustering in a cooperative manner was proposed [5]. A method bootstrap mean value where blocks were generated by substitution in the data set was proposed [6]. Considering the estimation of the average of random variables, if enough blocks were generated, the bootstrap median of the average had a better collapse point than the median of the average.…”

Section: Related Workmentioning

confidence: 99%

Recognition Model and Simulation of Busy Waters in Fishing Area Based on Density Clustering

Chai¹,

Chai²,

Xue³

et al. 2022

Journal of Compurters

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<p>In this paper, the characteristics of the potential behavior of ships contained in AIS information are con-sidered, in order to ensure the safety of navigation in merchant ships’ fishing areas and reduce the occur-rence of collisions between commercial fishing boats. Based on the DBSCAN density clustering algorithm, the identification model of busy water in fishing areas is developed and applied to Minnan fishery in the Taiwan Strait. In addition, a real ship simulation is performed based on real traffic flow data. The results demonstrate that the proposed model can accurately identify the spatial distribution and scale of busy fishing area, adjust the algorithm parameters according to the merchant ship scale, and generate the target-ed recommended route decision for the fishing area. Finally, the STELLAR EXPRESS is compared with the original route. The obtained results show that the recommended route provides a high safety in the fishing area, while retaining the ship operating costs. The model results can be used as a reference for maritime security departments in order to divide the fishing area warning water, and the identification method provides a novel approach for the safety supervision of maritime department. </p> <p> </p>

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“…Towards finding probabilistic error bounds, following research derived uniform concentration results for k-means and its variants (Telgarsky and Dasgupta, 2012), sub-Gaussian distortion bounds for the k-medians problem (Brownlees et al, 2015), and a O( log n/n) bound on k-means with Bregman divergences (Paul et al, 2021b). More recently, concentration inequalities for k-means under the MoM paradigm have been established (Klochkov et al, 2020;Brunet-Saumard et al, 2022) under the restriction that sample cluster centroids ( Θ n in Section 3) are assumed to be bounded. This paper shows how a number of center-based clustering methods can be brought under the same umbrella and can be robustified using a general-purpose scheme.…”

Section: Related Theoretical Analyses Of Clusteringmentioning

confidence: 99%

“…MoM estimators are not only insensitive to outliers, but are also equipped with exponential concentration results under the mild condition of finite variance (Lugosi and Mendelson, 2019;Lerasle, 2019;Laforgue et al, 2019). Recently, near-optimal results for mean estimation (Minsker, 2018), classification , regression (Mathieu and Minsker, 2021;Lugosi and Mendelson, 2019), clustering (Klochkov et al, 2020;Brunet-Saumard et al, 2022), bandits (Bubeck et al, 2013) and optimal transport (Staerman et al, 2021) have been established from this perspective.…”

Section: Introductionmentioning

confidence: 99%

Uniform Concentration Bounds toward a Unified Framework for Robust Clustering

Paul¹,

Chakraborty²,

Das³

et al. 2021

Preprint

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Recent advances in center-based clustering continue to improve upon the drawbacks of Lloyd's celebrated k-means algorithm over 60 years after its introduction. Various methods seek to address poor local minima, sensitivity to outliers, and data that are not well-suited to Euclidean measures of fit, but many are supported largely empirically. Moreover, combining such approaches in a piecemeal manner can result in ad hoc methods, and the limited theoretical results supporting each individual contribution may no longer hold. Toward addressing these issues in a principled way, this paper proposes a cohesive robust framework for center-based clustering under a general class of dissimilarity measures. In particular, we present a rigorous theoretical treatment within a Median-of-Means (MoM) estimation framework, showing that it subsumes several popular k-means variants. In addition to unifying existing methods, we derive uniform concentration bounds that complete their analyses, and bridge these results to the MoM framework via Dudley's chaining arguments. Importantly, we neither require any assumptions on the distribution of the outlying observations nor on the relative number of observations n to features p. We establish strong consistency and an error rate of O(n −1/2 ) under mild conditions, surpassing the best-known results in the literature. The methods are empirically validated thoroughly on real and synthetic datasets.

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K-bMOM: A robust Lloyd-type clustering algorithm based on bootstrap median-of-means

Cited by 12 publications

References 21 publications

Analysis and Application Research of E-Commerce Financial Management Based on T-DPC Optimization Algorithm

Analysis and Application Research of E-Commerce Financial Management Based on T-DPC Optimization Algorithm

Recognition Model and Simulation of Busy Waters in Fishing Area Based on Density Clustering

Uniform Concentration Bounds toward a Unified Framework for Robust Clustering

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