Abstract
This paper focuses on the covering mechanism which generates a new if-then rule when the input data does not match the rules in the XCS Classifier System (XCS), a rule-based machine learning system, and discusses how the new rule should be generated from the viewpoint of “inheritance” and “expansion” of the generalization degree of the nearest neighbor rule in the continuous space. For this purpose, this paper proposes the two covering mechanisms based on the “inheritance” and “expansion” of the generalization degree of the nearest neighbor rule and compares their results by applying them to XCS for real-valued input spaces (XCSR). Through the intensive experiments on three types of problems with the different characteristics, the following implications have been revealed: (1) the new rules should be generated by inheriting the generalization degree of the nearest neighbor rule in comparison with expanding it in the continuous space; and (2) XCSR with the “inheritance” based covering mechanism achieves higher classification accuracy with fewer rules than the conventional XCSR, which achieves higher classification accuracy than XCSR with the “expansion” based covering mechanism.
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Notes
- 1.
The experience exp, the time stamp ts, and the action set size as.
- 2.
To implement XCSR-LCGE and XCSR-LCGI, replace the function LocalCovering of XCS-LCPCI in [16] with Algorithm 1.
- 3.
For example, in the case of the bit sequence \(\boldsymbol{b}=11101010101\), \(d=(b_0b_1b_2)_{2}=(111)_{2}=7\), so the correct answer class is determined to be \(b_{k+d}=b_{3+7}=b_{10}=1\).
- 4.
- 5.
11-RMUX: \(N=20,000\), \(\alpha =0.1\), \(\beta =0.229242\), \(\delta =0.1\), \(\nu =5\), \(\theta _{mna}=2\), \(\theta _{GA}=12\), \(\theta _{del}=20\), \(\theta _{sub}=15\), \(\epsilon _0=109.918427\), \(\chi =0.8\), \(\mu =0.04\), \(p_I=0.01\), \(\epsilon _I=0.01\), \(F_I=0.01\), \(FitnessReduction=0.1\), \(m_0=0.1\), \(r_0=1.0\), \(doASSubsumption=yes\), \(doGASubsumption=yes\).
- 6.
6-IRMUX: Analogous to 11-RMUX, except: \(N=2000\), \(\beta =0.030691\), \(\theta _{GA}=192\), \(\theta _{sub}=217\), \(\epsilon _0=9.085638\), \(doASSubsumption=no\).
- 7.
Paddy Leaf: Analogous to 11-RMUX, except: \(N=6400\), \(\beta =0.2\), \(\theta _{mna}=4\), \(\theta _{GA}=48\), \(\theta _{del}=50\), \(\theta _{sub}=50\), \(\epsilon _0=1.0\), \(m_0=0.5\).
- 8.
For example, in the case of the 11-RMUX problem, the generality of each rule in the optimal ruleset [O] [4] is uniformly \(0.5^{k+1}=0.5^4=0.0625\), regardless of the class. Similarly, in the case of 6-IRMUX, it is uniformly \(0.5^{k+1}=0.5^3=0.125\).
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Shiraishi, H., Hayamizu, Y., Nakari, I., Sato, H., Takadama, K. (2022). Inheritance vs. Expansion: Generalization Degree of Nearest Neighbor Rule in Continuous Space as Covering Operator of XCS. In: Jiménez Laredo, J.L., Hidalgo, J.I., Babaagba, K.O. (eds) Applications of Evolutionary Computation. EvoApplications 2022. Lecture Notes in Computer Science, vol 13224. Springer, Cham. https://doi.org/10.1007/978-3-031-02462-7_23
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