Abstract
A quasi-physical algorithm was proposed for solving the linear separation problem of point set in n-dimensional space. The original idea of the quasi-physical algorithm is to find an equivalent physical world for the primitive mathematical problem and to observe the vivid images of the motion of matter in it so as to be inspired to obtain an algorithm for solving the mathematical problem. In this work, the electrostatics with two kinds of matter is found to be the equivalent physical world. As a result, the proposed algorithm is evidently more efficient and robust than the famous LMS algorithm and ETL algorithm. The efficiency of the quasiphysical algorithm is about 10 – 50 times of the LMS algorithm’s for representative instances. A typical Boolean-valued instance shows that it is hard for ETL algorithm but very easy for the quasi-physical algorithm. In this instance, point set A and B is {000, 010, 011, 111} and {001, 100}, respectively.
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References
Widrow B, Walach E. On the statistical efficiency of the LMS algorithm with nonstationary inputs [J]. IEEE Trans, IT, 1984, 3(2): 211–221
Kim J H, Park S K. The geometrical learning of binary neural networks [J]. IEEE Transactions on Neural Networks, 1995, 6(1):237–247
HUANG Wen-qi. A quasi-physical method for solving the covering problem—an approach to tackling NP-hard problems [J]. Abstracts of Papers Presented to the American Mathematical Society, 1988, 9(3):275
HUANG Wen-qi, ZHAN Shu-hao. A quasi-physical method of solving packing problems[J]. Mathematical Reviews of American Mathematical Society, 1982, 82h:52002
HUANG Wen-qi, WANG Gang-qiang. A quasi-mechanical method for solving the rectangle covering problem—an approach to tackling NP-hard problems [J]. Graphical Models and Image Processing, 1994, 56(3): 267–271
HUANG Wen-qi, ZHAN Shu-hao. A quasi-physical method for solving the packing problem [J]. Acta Math Appl Sinica (in Chinese), 1979, 2(2): 176–180
HUANG Wen-qi. A quasi-physical method for solving the covering problem—an approach to tackling NP-hard problems [J]. Chinese Journal of Computers (in Chinese), 1989, 12(8): 610–616
Li Wei, HUANG Wen-qi. A mathematic-physical approach to the satisfiability problem [J]. Science in China (series A), 1995, 38(1):116–128
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Foundation item: The National Key Basic Research Program (973) (No. G 1998030600)
Biography of the author: HUANG Jia-yuan, born in 1979, majoring in intelligent computing.
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Huang, Jy. A quasi-physical algorithm for solving the linear separation problem in n-dimensional space. J Cent. South Univ. Technol. 8, 272–277 (2001). https://doi.org/10.1007/s11771-001-0069-5
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DOI: https://doi.org/10.1007/s11771-001-0069-5