HD-NSA: A real-valued negative selection algorithm based on hierarchy division

The negative selection algorithm (NSA) is an important algorithm for generating immune detectors in artificial immune systems. However, the original NSA randomly generates candidate detectors that produce a large number of redundant detectors, and it is difficult to cover the entire antibody space. Moreover, the randomly generated candidate detectors have to be compared with all the self-sets; therefore, the inefficient generation of the detector seriously influences the application of NSA. To overcome these defects, a real-valued NSA based on hierarchy division (HD-NSA) is proposed. First, the feature space is divided into self and non-self subgrids, and the center point of the non-self subgrid is specified as the candidate detector, and the specified candidate detector is compared with the self-antigens located in adjacent subgrids rather than with all the self-sets. Theoretical analysis demonstrated that the HD-NSA can effectively reduce the time complexity of the NSA algorithm. Furthermore, experiments on the Abalone data set show that the detector training time of HD-NSA decreased by 97.9%, 71.2%, 56.9% and 90.1%, respectively, compared with the classical RNSA, V-Detector, GF-RNSA and BIORV-NSA, whereas the detector detection rate increased by 50%, 25.8%, 13.8% and 10.5%, respectively. (C) 2021 Elsevier B.V. All rights reserved.