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- W2152523366 abstract "An implicit Lagrangian for the dual of a simple reformulation of the standard quadratic program of a linear support vector machine proposed. This leads to the minimization of an unconstrained differentiable convex function in a space of dimensionality equal to the number of classified points. This problem solvable by an extremely simple linearly convergent Lagrangian support vector machine (LSVM) algorithm. LSVM requires the inversion at the outset of a single matrix of the order of the much smaller dimensionality of the original input space plus one. The full algorithm given in this paper in 11 lines of MATLAB code without any special optimization tools such linear or quadratic programming solvers. This LSVM code can be used as is to solve classification problems with millions of points. For example, 2 million points in 10 dimensional input space were classified by a linear surface in 82 minutes on a Pentium III 500 MHz notebook with 384 megabytes of memory (and additional swap space), and in 7 minutes on a 250 MHz UltraSPARC II processor with 2 gigabytes of memory. Other standard classification test problems were also solved. Nonlinear kernel classification can also be solved by LSVM. Although it does not scale up to very large problems, it can handle any positive semidefinite kernel and guaranteed to converge. A short MATLAB code also given for nonlinear kernels and tested on a number of problems." @default.
- W2152523366 created "2016-06-24" @default.
- W2152523366 date "2000-01-01" @default.
- W2152523366 modified "2023-10-18" @default.
- W2152523366 title "10.1162/15324430152748218" @default.
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- W2152523366 doi "https://doi.org/10.1162/15324430152748218" @default.
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