RECORD
Kernel Bandwidth Selection for SVDD: Peak Criterion Approach for Large Data
Machine Learning · Submitted 31 Oct 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Empirical comparison demonstrates the advantage of the proposed method.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. Gaussian kernel used in SVDD formulation allows flexible data description defined by observations designated as support vectors. The data boundary of such description is non-spherical and conforms to the geometric features of the data. By varying the Gaussian kernel bandwidth parameter, the SVDD-generated boundary can be made either smoother (more spherical) or tighter/jagged. The former case may lead to under-fitting, whereas the latter may result in overfitting. Peak criterion has been proposed to select an optimal value of the kernel bandwidth to strike the balance between the data boundary smoothness and its ability to capture the general geometric shape of the data. Peak criterion involves training SVDD at various values of the kernel bandwidth parameter. When training datasets are large, the time required to obtain the optimal value of the Gaussian kernel bandwidth parameter according to Peak method can become prohibitively large. This paper proposes an extension of Peak method for the case of large data. The proposed method gives good results when applied to several datasets. Two existing alternative methods of computing the Gaussian kernel bandwidth parameter (Coefficient of Variation and Distance to the Farthest Neighbor) were modified to allow comparison with the proposed method on convergence. Empirical comparison demonstrates the advantage of the proposed method.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. | background 1.00 | 0.05 | 0.02 | asserted 0.99 |
| s1 | Gaussian kernel used in SVDD formulation allows flexible data description defined by observations designated as support vectors. | background 0.99 | 0.06 | 0.02 | asserted 1.00 |
| s2 | The data boundary of such description is non-spherical and conforms to the geometric features of the data. | background 1.00 | 0.10 | 0.02 | asserted 1.00 |
| s3 | By varying the Gaussian kernel bandwidth parameter, the SVDD-generated boundary can be made either smoother (more spherical) or tighter/jagged. | background 1.00 | 0.13 | 0.03 | asserted 0.64 |
| s4 | The former case may lead to under-fitting, whereas the latter may result in overfitting. | background 0.97 | 0.09 | 0.02 | hedged possibility 1.00 |
| s5 | Peak criterion has been proposed to select an optimal value of the kernel bandwidth to strike the balance between the data boundary smoothness and its ability to capture the general geometric shape of the data. | background 0.92 | 0.07 | 0.09 | asserted 1.00 |
| s6 | Peak criterion involves training SVDD at various values of the kernel bandwidth parameter. | background 0.60 | 0.12 | 0.02 | asserted 1.00 |
| s7 | When training datasets are large, the time required to obtain the optimal value of the Gaussian kernel bandwidth parameter according to Peak method can become prohibitively large. | gap 0.48 | 0.24 | 0.03 | hedged possibility 0.76 |
| s8 | This paper proposes an extension of Peak method for the case of large data. | contribution 1.00 | 0.86 | 0.13 | asserted 1.00 |
| s9 | The proposed method gives good results when applied to several datasets. | result 0.99 | 0.91 | 0.41 | asserted 0.98 |
| s10 | Two existing alternative methods of computing the Gaussian kernel bandwidth parameter (Coefficient of Variation and Distance to the Farthest Neighbor) were modified to allow comparison with the proposed method on convergence. | method 0.79 | 0.87 | 0.04 | asserted 0.96 |
| s11 | Empirical comparison demonstrates the advantage of the proposed method. | result 0.90 | 0.93 | 0.62 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. Gaussian kernel used in SVDD formulation allows flexible data description defined by observations designated as support vectors. The data boundary of such description is non-spherical and conforms to the geometric features of the data. By varying the Gaussian kernel bandwidth parameter, the SVDD-generated boundary can be made either smoother (more spherical) or tighter/jagged. The former case may lead to under-fitting, whereas the latter may result in overfitting. Peak criterion has been proposed to select an optimal value of the kernel bandwidth to strike the balance between the data boundary smoothness and its ability to capture the general geometric shape of the data. Peak criterion involves training SVDD at various values of the kernel bandwidth parameter. When training datasets are large, the time required to obtain the optimal value of the Gaussian kernel bandwidth parameter according to Peak method can become prohibitively large. This paper proposes an extension of Peak method for the case of large data. The proposed method gives good results when applied to several datasets. Two existing alternative methods of computing the Gaussian kernel bandwidth parameter (Coefficient of Variation and Distance to the Farthest Neighbor) were modified to allow comparison with the proposed method on convergence. Empirical comparison demonstrates the advantage of the proposed method.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.