A Real-Valued Negative Selection Algorithm Based on Grid for Anomaly Detection

Algorithm 2

The algorithm of GB-RNSA.

𝐺𝐵-𝑅𝑁𝑆𝐴(𝑇𝑟𝑎𝑖𝑛,𝐶_exp,𝐷)

Input: the self training set 𝑇𝑟𝑎𝑖𝑛, expected coverage 𝐶_exp

Output: the detector set 𝐷

𝑁₀: sampling times in non-self space, 𝑁₀>max(5/𝐶_exp,5/(1−𝐶_exp))

𝑖: the number of non-self samples

𝑥: the number of non-self samples covered by detectors

𝐶𝐷: the set of candidate detectors 𝐶𝐷={𝑑∣𝑑=<𝑦₁,𝑦₂,…,𝑦_𝑛,𝑟_𝑑>,𝑦_𝑗∈[0,1],1≤𝑗≤𝑛,𝑟_𝑑∈[0,1]}

Step 1. Initialize the self training set 𝑇𝑟𝑎𝑖𝑛,𝑖=0,𝑥=0,𝐶𝐷=∅,𝑁₀=𝑐𝑒𝑖𝑙𝑖𝑛𝑔(max(5/𝐶_exp,5/(1−𝐶_exp)))

Step 2. Call 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝐺𝑟𝑖𝑑(𝑇𝑟𝑎𝑖𝑛,𝑇𝑟𝑒𝑒𝐺𝑟𝑖𝑑,𝐿𝑖𝑛𝑒𝐺𝑟𝑖𝑑𝑠) to generate grid structure which contains selves, where

    𝑇𝑟𝑒𝑒𝐺𝑟𝑖𝑑 is the 2^𝑛-tree storage of grids and 𝐿𝑖𝑛𝑒𝐺𝑟𝑖𝑑𝑠 is the line storage of grids;

Step 3. Randomly generate a candidate detector 𝑑_new. Call 𝐹𝑖𝑛𝑑𝐺𝑟𝑖𝑑(𝑑_new,𝑇𝑟𝑒𝑒𝐺𝑟𝑖𝑑,𝑇𝑒𝑚𝑝𝐺𝑟𝑖𝑑) to find the grid

    𝑇𝑒𝑚𝑝𝐺𝑟𝑖𝑑 where 𝑑_new is;

Step 4. Calculate the Euclidean distance between 𝑑_new and all the selves in 𝑇𝑒𝑚𝑝𝐺𝑟𝑖𝑑 and its neighbor grids. If

    𝑑_new is identified by a self antigen, abandon it and execute Step 3; if not, increase 𝑖;

Step 5. Calculate the Euclidean distance between 𝑑_new and all the detectors in 𝑇𝑒𝑚𝑝𝐺𝑟𝑖𝑑 and its neighbor grids. If

    𝑑_new is not identified by any detector, add it into the candidate detector set 𝐶𝐷; if not, increase 𝑥, and judge

    whether it reaches the expected coverage 𝐶_exp, if so, return 𝐷 and the algorithm ends;

Step 6. Judge whether 𝑖 reaches sampling times 𝑁₀. If 𝑖=𝑁₀, call 𝐹𝑖𝑙𝑡𝑒𝑟(𝐶𝐷) to implement the screening process of

   candidate detectors, and put candidate detectors which passed this process into 𝐷, reset 𝑖,𝑥,𝐶𝐷;

    if not, return to Step 3.