Kernel Methods for Implicit Surface Modeling
B. Scholkopf, J. Giesen, S. Spalinger
r92922120 黃邦洪r93922020 楊惠菁r93922038 柯政宏r93944009 劉弘偉
Outline
Introduction Single-Class SVMs Slab SVMs Epsilon-SVR Implement Result
Introduction
Step 1: Given a finite sample points belong to some
hypersurface in Euclidean space R3
The sample can be very large, noisy or sparse
Introduction
Step 2: Use SVM to find an implicit surface
f is the decision function in SVM
The zero set of f is a surface that approximates
the sample points
Single-Class SVM v.s. Slab SVM
3:f
)0(1f
Outline
Introduction Single-Class SVMs Slab SVMs Epsilon-SVR Implement Result
Single-Class SVM
Primary Object function
Concept
Single-Class SVM
Dual Problem
Decision function
Single-Class SVM
SVM TOY example
Outline
Introduction Single-Class SVMs Slab SVMs Epsilon-SVR Implement Result
Slab SVM
Primary object function
Concept
Slab SVM
Lagrangian dual optimization problem
Decision function
Slab SVM
SVM TOY example
Outline
Introduction Single-Class SVMs Slab SVMs Epsilon-SVR Implement Result
Epsilon-SVR
Primary object function
Concept
Epsilon-SVR
Lagrangian dual optimization problem
The approximate function
Outline
Introduction Single-Class SVMs Slab SVMs Epsilon-SVR Implement Result
Implement
Single-Class SVM Use LIBSVM directly
Slab-SVM Modify epsilon-SVR in LIBSVM to slab-SVM The result is parameter-sensitive Modification:
decision function
The result is good but we don’t really know how to explain
Outline
Introduction Single-Class SVMs Slab SVMs Epsilon-SVR Implement Result
Result(1) - One-Class SVM
Bunny Original: 35947 One-Class: 2810
Result(1) - Slab SVM
Bunny Left: 8307。 Right: 1013
Result(1) - Slab SVM
Bunny Predict accuracy: 97.74%
Result(2) - One-Class SVM
Cactus Original: 3337 One-Class: 1617
Result(2) - Slab SVM
Cactus Left: 996 Right: 817
Result(2) - Slab SVM
Cactus Predict accuracy: 96.9434%
Result(3) - One-Class SVM
Dinosaur Original: 56194 One-Class: 44963
Result(3) - Slab SVM
Dinosaur Left: 13005。 Right: 1018
Result(3) - Slab SVM
Dinosaur Predict accuracy: 97.43%
Result(4) - One-Class SVM
Knot Original: 10000 One-Class: 8807
Result(4) - Slab SVM
Knot Left: 1176。 Right: 1036
Result(4) - Slab SVM
Knot Predict accuracy: 96.9%
Result(5) - One-Class SVM
Screwdriver Original: 27152 One-Class:21728
Result(5) - Slab SVM
Screwdriver Left: 6574 Right: 884
Result(5) - Slab SVM
Screwdriver Predict accuracy: 97.1752%
Result(6) - One-Class SVM
Rockerarm Original: 40177 One-Class: 4868
Result(6) - Slab SVM
Rockerarm Left: 2090 Right: 1029
Result(6) - Slab SVM
Rocker arm Predict accuracy: 96.18%
Result(7) - One-Class SVM
Hole Original: 4000 One-Class: 3224
Result(7) - Slab SVM
Hole Left: 648 Right:1039
Result(7) - Slab SVM
Hole Predict accuracy: 93.475%
Q&A
Thank You
