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| Hiroshi Hirai, Kazuo Murota and Masaki Rikitoku | ||||||
| Key words: | ||||||
| upport vector machine (SVM), discrete kernel, discrete Green's function, tree metric, electric network, inverse M-matrix | ||||||
| Mathematices Subject Classification: 90C90, 68T05 | ||||||
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| Hiroshi Hirai, Kazuo Murota and Masaki Rikitoku | ||||||
| Key words: | ||||||
| upport vector machine (SVM), discrete kernel, discrete Green's function, tree metric, electric network, inverse M-matrix | ||||||
| Mathematices Subject Classification: 90C90, 68T05 | ||||||
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| Abstract: | |||
| This paper investigates support vector machine (SVM) with a discrete kernel, named electric network kernel, defined on the vertex set of an undirected graph. Emphasis is laid on mathematical analysis of its theoretical properties with the aid of electric network theory and the theory of discrete metrics. SVM with this kernel admits physical interpretations in terms of resistive electric networks; in particular, the SVM decision function corresponds to an electric potential. Preliminary computational results indicate reasonable promise of the proposed kernel in comparison with the Hamming and diffusion kernels. | |||
| SVM kernel by electric network score | ||
| Special Issue in Honor of the 65th Birthday of Toshihide Ibaraki | |||
| Volume 1, Number 3, September 2005, pp. 509-526 | |||