Theoretical formulation and analysis of the deterministic dendritic cell algorithm

Gu, Feng; Greensmith, Julie; Aickelin, Uwe

Abstract

As one of the emerging algorithms in the field of artificial 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 definition, 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 definition of the algorithm, as well as to perform runtime analyses to reveal its theoretical aspects. In this paper, we define 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)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))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.

Citation

Gu, F., Greensmith, J., & Aickelin, U. (2013). Theoretical formulation and analysis of the deterministic dendritic cell algorithm. BioSystems, 111(2), 127-135. https://doi.org/10.1016/j.biosystems.2013.01.001

• Journal Article Type: Article
• Acceptance Date: Jan 4, 2013
• Online Publication Date: Jan 18, 2013
• Publication Date: Feb 1, 2013
• Deposit Date: Sep 27, 2014
• Publicly Available Date: Sep 27, 2014
• Journal: Biosystems
• Print ISSN: 0303-2647
• Electronic ISSN: 0303-2647
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 111
• Issue: 2
• Pages: 127-135
• DOI: https://doi.org/10.1016/j.biosystems.2013.01.001
• Keywords: Artificial Immune Systems, Biomedical Informatics; Dendritic cell algorithm; Runtime analysis; Formulation and formalisation
• Public URL: https://nottingham-repository.worktribe.com/output/1002833
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0303264713000063
• Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Biosystems. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Biosystems, 111(2), (2013), doi: 10.1016/j.biosystems.2013.01.001