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) 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.
Highlights
Artificial Immune Systems (AIS) [7, 18] are computer systems inspired by both theoretical immunology and observed immune functions, principles and models, which are applied to real-world problems
This aims to present the algorithm in a comprehensive way, which can be accessed by readers who may not be familiar with formal logic
We provide formal definitions of the data structures and procedural operations of the deterministic version of the Dendritic Cell Algorithm (DCA), name the deterministic DCA (dDCA)
Summary
Artificial Immune Systems (AIS) [7, 18] are computer systems inspired by both theoretical immunology and observed immune functions, principles and models, which are applied to real-world problems. The resulting algorithms are believed to encapsulate the desirable properties of immune systems, including robustness, error tolerance, and self-organisation [7] One such ‘second generation’ immune algorithms is the Dendritic Cell Algorithm (DCA) [10]. One criticism is the lack of a formal definition, which could result in ambiguity for understanding the algorithm and lead to incorrect applications and implementations It is pointed out in [28] that the DCA shares similarities to linear classifiers since it employs a linear discriminant function for signal transformation. It is important to conduct a similar theoretical analysis of the DCA, to determine its runtime complexity and numerous other algorithmic properties, in line with other AIS. The aim is to provide a clear and accessible definition of the DCA, as well as an initial theoretical analysis on the algorithm’s runtime complexity and other algorithmic properties.
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