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Voronoi Boundary Classification:
A High-Dimensional Geometric Approach via Weighted Monte Carlo Integration
Voronoi Boundary Classification: A High-Dimensional Geometric - - PowerPoint PPT Presentation
Voronoi Boundary Classification: A High-Dimensional Geometric - - PowerPoint PPT Presentation
Voronoi Boundary Classification: A High-Dimensional Geometric Approach via Weighted Monte Carlo Integration Vladislav Polianskii, Florian T. Pokorny w ( z ) = exp ( 0 . 5 z 2 0 . 1 2 ) w ( z ) = exp ( 0 . 5 z 2 1 2 ) w ( z ) = exp
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−4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 3.5 4 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 3.5 4 w(z) = exp(−0.5z20.1−2)
z2−4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 3.5 4 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 3.5 4 w(z) = exp(−0.5z21−2)
z2−4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 3.5 4 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 3 3.5 4 w(z) = exp(−0.5z210−2)
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Evaluation results
Comparison with other classical ML methods (no data preprocessing): Running time on CIFAR with 10 000 samples on GPU: ~5 min.
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Accuracy convergence
MNIST CIFAR10
0.2 0.4 0.6 0.8 1 ·104 0.964 0.965 0.966 0.967 0.968 0.969 0.970 0.2 0.4 0.6 0.8 1 ·104 0.325 0.350 0.375 0.400 0.425 0.450 0.475 0.500
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