Theoretical formulation and analysis of the deterministic dendritic cell algorithm

As one of the emerging algorithms in the eld of Articial Immune Systems(AIS), the Dendritic Cell Algorithm (DCA) has been successfully applied to a number of challenging real-world problems. However, one criticism is the lack of a formal denition, which could result in ambiguity for understanding th...

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Main Authors:	Gu, Feng, Greensmith, Julie, Aickelin, Uwe
Format:	Article
Language:	English
Published:	2013
Online Access:	http://eprints.nottingham.ac.uk/2071/ http://eprints.nottingham.ac.uk/2071/ http://eprints.nottingham.ac.uk/2071/ http://eprints.nottingham.ac.uk/2071/1/Theoretical_Formulation_%26_Anaylsis_of_the_Deterministic_Dendritic_Cell_Algorithm.Biosystems_111%282%29.2013.pdf

id	nottingham-2071
recordtype	eprints
spelling	nottingham-20712017-10-14T06:08:41Z http://eprints.nottingham.ac.uk/2071/ Theoretical formulation and analysis of the deterministic dendritic cell algorithm Gu, Feng Greensmith, Julie Aickelin, Uwe As one of the emerging algorithms in the eld of Articial Immune Systems(AIS), the Dendritic Cell Algorithm (DCA) has been successfully applied to a number of challenging real-world problems. However, one criticism is the lack of a formal denition, which could result in ambiguity for understanding the algorithm. Moreover, previous investigations have mainly focused on its empirical aspects. Therefore, it is necessary to provide a formal def- inition of the algorithm, as well as to perform runtime analyses to reveal its theoretical aspects. In this paper, we dene the deterministic version of the DCA, named the dDCA, using set theory and mathematical functions. Runtime analyses of the standard algorithm and the one with additional segmentation are performed. Our analysis suggests that the standard dDCA has a runtime complexity of O(n2) for the worst-case scenario, where n is the number of input data instances. The introduction of segmentation changes the algorithm's worst case runtime complexity to O(max(nN; nz)), for DC population size N with size of each segment z. Finally, two runtime variables of the algorithm are formulated based on the input data, to understand its runtime behaviour as guidelines for further development. 2013 Article PeerReviewed application/pdf en http://eprints.nottingham.ac.uk/2071/1/Theoretical_Formulation_%26_Anaylsis_of_the_Deterministic_Dendritic_Cell_Algorithm.Biosystems_111%282%29.2013.pdf Gu, Feng and Greensmith, Julie and Aickelin, Uwe (2013) Theoretical formulation and analysis of the deterministic dendritic cell algorithm. Biosystems, 111 (2). pp. 127-135. ISSN 0303-2647 http://www.sciencedirect.com/science/article/pii/S0303264713000063# doi:10.1016/j.biosystems.2013.01.001 doi:10.1016/j.biosystems.2013.01.001
repository_type	Digital Repository
institution_category	Local University
institution	University of Nottingham Malaysia Campus
building	Nottingham Research Data Repository
collection	Online Access
language	English
description	As one of the emerging algorithms in the eld of Articial Immune Systems(AIS), the Dendritic Cell Algorithm (DCA) has been successfully applied to a number of challenging real-world problems. However, one criticism is the lack of a formal denition, which could result in ambiguity for understanding the algorithm. Moreover, previous investigations have mainly focused on its empirical aspects. Therefore, it is necessary to provide a formal def- inition of the algorithm, as well as to perform runtime analyses to reveal its theoretical aspects. In this paper, we dene the deterministic version of the DCA, named the dDCA, using set theory and mathematical functions. Runtime analyses of the standard algorithm and the one with additional segmentation are performed. Our analysis suggests that the standard dDCA has a runtime complexity of O(n2) for the worst-case scenario, where n is the number of input data instances. The introduction of segmentation changes the algorithm's worst case runtime complexity to O(max(nN; nz)), for DC population size N with size of each segment z. Finally, two runtime variables of the algorithm are formulated based on the input data, to understand its runtime behaviour as guidelines for further development.
format	Article
author	Gu, Feng Greensmith, Julie Aickelin, Uwe
spellingShingle	Gu, Feng Greensmith, Julie Aickelin, Uwe Theoretical formulation and analysis of the deterministic dendritic cell algorithm
author_facet	Gu, Feng Greensmith, Julie Aickelin, Uwe
author_sort	Gu, Feng
title	Theoretical formulation and analysis of the deterministic dendritic cell algorithm
title_short	Theoretical formulation and analysis of the deterministic dendritic cell algorithm
title_full	Theoretical formulation and analysis of the deterministic dendritic cell algorithm
title_fullStr	Theoretical formulation and analysis of the deterministic dendritic cell algorithm
title_full_unstemmed	Theoretical formulation and analysis of the deterministic dendritic cell algorithm
title_sort	theoretical formulation and analysis of the deterministic dendritic cell algorithm
publishDate	2013
url	http://eprints.nottingham.ac.uk/2071/ http://eprints.nottingham.ac.uk/2071/ http://eprints.nottingham.ac.uk/2071/ http://eprints.nottingham.ac.uk/2071/1/Theoretical_Formulation_%26_Anaylsis_of_the_Deterministic_Dendritic_Cell_Algorithm.Biosystems_111%282%29.2013.pdf
first_indexed	2018-09-06T10:20:58Z
last_indexed	2018-09-06T10:20:58Z
_version_	1610853130998644736

Theoretical formulation and analysis of the deterministic dendritic cell algorithm

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