kernel methods for implicit surface modeling b. scholkopf, j. giesen, s. spalinger
DESCRIPTION
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: - PowerPoint PPT PresentationTRANSCRIPT
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