DocumentCode :
2361371
Title :
Stability analysis of the decomposition method for solving support vector machines
Author :
Lai, D. ; Shilton, A. ; Mani, N. ; Paianiswami, M.
Author_Institution :
Dept. of Electr. & Comput. Syst. Eng., Monash Univ., Clayton, Vic., Australia
fYear :
2005
fDate :
4-7 Jan. 2005
Firstpage :
272
Lastpage :
277
Abstract :
In situations where processing memory is limited, the Support Vector Machine quadratic program can be decomposed into smaller sub-problems and solved sequentially. The convergence of this method has been proven previously through (he use of a counting method. In this initial investigation, we approach the convergence analysis by treating the decomposed sub-problems as subsystems of a general system. The gradients of the sub-problems and the inequality constraints are explicitly modelled as system variables. The change in these variables during optimization form a dynamic system modelled by vector differential equations. We show that the change in the objective function can be written as the energy in the system. This makes it a natural Lyapunov function, which has an asymptotically stable point at the origin. The asymptotic stability of the whole system then follows under certain assumptions.
Keywords :
Lyapunov methods; asymptotic stability; convergence; differential equations; quadratic programming; support vector machines; asymptotic stability analysis; convergence; decomposition method; dynamic system; natural Lyapunov function; optimization; processing memory; quadratic program; support vector machine; vector differential equation; Convergence; Kernel; Lagrangian functions; Pattern recognition; Quadratic programming; Stability analysis; Supervised learning; Support vector machine classification; Support vector machines; Systems engineering and theory;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Intelligent Sensing and Information Processing, 2005. Proceedings of 2005 International Conference on
Print_ISBN :
0-7803-8840-2
Type :
conf
DOI :
10.1109/ICISIP.2005.1529461
Filename :
1529461
Link To Document :
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