Abstract
In pattern classification, the geometric method often provides a simple and intuitive solution. In the case of linear separability, solving the optimization hyperplane problem can be transformed into solving the nearest point problem of the convex hulls between classes. In the case of nonlinear separability, the notion of scaled convex hull (SCH) is employed to reduce the initially overlapping convex hulls to become separable. Two classic nearest point algorithms, GSK and MDM, have been used as effective solvers for SCHs. However, their problem-solving speed is still a bit underperforming. This paper proposes a new solver called SCH-CDM, in which the CDM (cross distance minimization) algorithm is employed to calculate the nearest point pair of between-class SCHs. Experimental results indicate that the SCH-CDM algorithm can achieve faster convergence than the SCH-GSK algorithm and the SCH-MDM algorithm. In terms of accuracy, it also shows good competitiveness compared to the baseline methods.
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Leng, Q., Jiao, E., Liu, Y., Guo, J., Chen, Y. (2022). Cross Distance Minimization for Solving the Nearest Point Problem Based on Scaled Convex Hull. In: Huang, DS., Jo, KH., Jing, J., Premaratne, P., Bevilacqua, V., Hussain, A. (eds) Intelligent Computing Methodologies. ICIC 2022. Lecture Notes in Computer Science(), vol 13395. Springer, Cham. https://doi.org/10.1007/978-3-031-13832-4_17
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