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PerTurbo: a new classification algorithm based on the spectrum perturbations of the Laplace-Beltrami operator
Published on Oct 03, 20113271 Views
PerTurbo, an original, non-parametric and efficient classification method is presented here. In our framework, the manifold of each class is characterized by its Laplace-Beltrami operator, which is
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Chapter list
PerTurbo: a new classi cation algorithm based on the spectrum perturbations of the Laplace-Beltrami operator00:00
Problem and motivations00:19
Outline01:10
Outline: Sampling problems in computer graphics01:33
Sampling point clouds in computer graphics01:34
Spectral sampling02:35
Riemanian manifolds and the Laplace-Beltrami Operator03:26
Approximating the Laplace-Beltrami operator04:17
Outline: Application to machine learning and classi cation05:03
Idea #1: Comparing a class to a surface (1)05:18
Idea #1: Comparing a class to a surface (2)05:45
Idea #1: Comparing a class to a surface (3)05:59
Idea #1: Comparing a class to a surface (4)06:16
Idea #1: Comparing a class to a surface (5)06:30
Idea #1: Comparing a class to a surface (6)06:44
Idea #2: Class-wise manifold learning07:10
Remarks and notations07:54
The perturbation measure in the Gaussian RKHS (1) (a)08:44
The perturbation measure in the Gaussian RKHS (1) (b)09:10
The perturbation measure in the Gaussian RKHS (1) (c)09:36
The perturbation measure in the Gaussian RKHS (2) (a)10:00
The perturbation measure in the Gaussian RKHS (2) (b)10:03
The perturbation measure in the Gaussian RKHS (2) (c)10:08
The perturbation measure in the Gaussian RKHS (2) (d)10:15
The perturbation measure in the Gaussian RKHS (2) (e)10:21
The perturbation measure in the Gaussian RKHS (2) (f)10:37
PerTurbo: A new classi cation algorithm (1)11:25
PerTurbo: A new classi cation algorithm (2)11:41
PerTurbo: A new classi cation algorithm (3)12:02
Outline: Experimental results12:42
Experimental setting and analysis of the results (1)12:45
Experimental setting and analysis of the results (2)13:33
Accuracy rates14:29
Outline: Future works15:05
Active Learning (1) (a)15:07
Active Learning (1) (b)15:30
Active Learning (2)15:50
Others16:04
Outline: Conclusion17:27
PerTurbo: Main results17:29
Thank you!17:48
Datasets18:18