Kernel Estimators in Industrial Applications

Kulczycki, Piotr

doi:10.1007/978-3-540-77465-5_4

Cited by 26 publications

(16 citation statements)

References 10 publications

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“…For the experiments a Gaussian kernel was used and smoothing parameter h was established using commonly used Silverman's "rule of thumb" [29]. As random sampling and K-means contain randomized component we used 30 replicates and report ISE mean and standard deviation.…”

Section: Future Challenges and Suggested Algorithmsmentioning

confidence: 99%

Survey of Object-Based Data Reduction Techniques in Observational Astronomy

et al. 2016

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Abstract:Dealing with astronomical observations represents one of the most challenging areas of big data analytics. Besides huge variety of data types, dynamics related to continuous data flow from multiple sources, handling enormous volumes of data is essential. This paper provides an overview of methods aimed at reducing both the number of features/attributes as well as data instances. It concentrates on data mining approaches not related to instruments and observation tools instead working on processed object-based data. The main goal of this article is to describe existing datasets on which algorithms are frequently tested, to characterize and classify available data reduction algorithms and identify promising solutions capable of addressing present and future challenges in astronomy.

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Section: Future Challenges and Suggested Algorithmsmentioning

confidence: 99%

Survey of Object-Based Data Reduction Techniques in Observational Astronomy

et al. 2016

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“…All the necessary details on the methods as well as details on deriving particular formulas can be found in many source materials (e.g., Silverman, 1986;Simonoff, 1996;Wand and Jones, 1995). Particular formulas for PLUGIN and LSCV_h approaches were adopted directly from Kulczycki (2005;2008) with only a slight change in some symbols to make them compatible with the classical book by Wand and Jones (1995).…”

Section: 2mentioning

confidence: 99%

Graphics processing units in acceleration of bandwidth selection for kernel density estimation

Andrzejewski¹,

Gramacki²,

Gramacki³

2013

International Journal of Applied Mathematics and Computer Science

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The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.

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“…Detailed information regarding kernel estimators can be found in the monographs [11,21,25]. Example practical applications are presented in the publications [12,13].…”

Section: Statistical Kernel Estimatorsmentioning

confidence: 99%

“…The obtained number of clusters was satisfying, which led to any possible change in the value of the smoothing parameter h becoming redundant. Finally, the sample, considered at this stage, containing 1639 elements was divided into 26 clusters of the following sizes: 488,413,247,128,54,41,34,34,33,28,26,21,20,14,13,12,10, two 4-element clusters, three of 3-elements, two of 2-elements and two of 1-element. It is worth noting the four clearly drawn groups: the first of these comprises two numerous clusters of 488 and 413-elements, next two medium-sized 247-and 128-elements, followed by small -nine clusters containing from 20 to 54 and lastly 13 clusters of less than 20 elements.…”

Section: Marketing Support Strategy For Mobile Phone Operatormentioning

confidence: 99%

The Complete Gradient Clustering Algorithm: properties in practical applications

Kulczycki

Charytanowicz

Kowalski

et al. 2012

Journal of Applied Statistics

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The aim of this paper is to present a Complete Gradient Clustering Algorithm, its applicational aspects and properties, as well as to illustrate them with specific practical problems from the subject of bioinformatics (the categorization of grains for seed production), management (the design of a marketing support strategy for a mobile phone operator) and engineering (the synthesis of a fuzzy controller). The main property of the Complete Gradient Clustering Algorithm is that it does not require strict assumptions regarding the desired number of clusters, which allows to better suit its obtained number to a real data structure. In the basic version it is possible to provide a complete set of procedures for defining the values of all functions and parameters relying on the optimization criterions. It is also possible to point out parameters, the potential change which implies influence on the size of the number of clusters (while still not giving an exact number) and the proportion between their numbers in dense and sparse areas of data elements. Moreover, the Complete Gradient Clustering Algorithm can be used to identify and possibly eliminate atypical elements (outliers). These properties proved to be very useful in the presented applications and may also be functional in many other practical problems.

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Kernel Estimators in Industrial Applications

Cited by 26 publications

References 10 publications

Survey of Object-Based Data Reduction Techniques in Observational Astronomy

Survey of Object-Based Data Reduction Techniques in Observational Astronomy

Graphics processing units in acceleration of bandwidth selection for kernel density estimation

The Complete Gradient Clustering Algorithm: properties in practical applications

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