Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines

Yeqian Liu

doi:doi:10.11648/j.ijdsa.20190503.12

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Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines

Yeqian Liu

Published in International Journal of Data Science and Analysis (Volume 5, Issue 3)

Received: 30 June 2019 Accepted: 24 July 2019 Published: 7 August 2019

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Abstract

The support vector machine (SVM) has become very popular within the machine learning literature. Recently, SVM has received much attention from statisticians. It is well known that for multicategory classification problem, the commonly used multicategory SVM is based on the frequentist framework. In this paper, we develop a multi-class support vector machine under the Bayesian framework. Numerical studies were performed by EM and the Bayesian algorithm Gibbs sampler. Our results have shown that the classification accuracy of the Bayesian approach is comparable to that of frequentist approaches, while Bayesian approach also has the advantage of providing estimates of uncertainty in predictions.

Published in	International Journal of Data Science and Analysis (Volume 5, Issue 3)
DOI	10.11648/j.ijdsa.20190503.12
Page(s)	42-51
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Multivariate Classifcation, MSVM, MCMC, EM

References

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[2]	Vapnik, V. (1998). Statistical learning theory. Wiley, New York.
[3]	Burges, C. J. C. (1998). A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2), 121-167.
[4]	Nicholas G. Polson and Steven L. Scott (2011). Data Augmentation for Support Vector Machines. Bayesian Analysis, 6, 1-24.
[5]	Cortes, C., Vapnik, V. (1995) Support-Vector Networks, Machine Learning.
[6]	Henao, R., Yuan, X., Carin, L. (2014) Bayesian Nonlinear Support Vector Machines and Discriminative Factor Modeling. Neural Information Processing Systems Conference.
[7]	Hoffman, M. D., Blei, D. M., Wang, C., Paisley, J. (2013) Stochastic Variational Inference. Journal of Machine Learning Research, 14, 1303-1347.
[8]	Hensman, J., Fusi, N., Lawrence, N. D. (2013) Gaussian processes for big data. Conference on Uncertainty in Artificial Intellegence.
[9]	Fernández-Delgado, M., Cernadas, E., Barro, S., Amorim, D. (2014) Do we need hundreds of classifiers to solve real world classification problems? Journal of Machine Learning Research, 15, 3133-3181.
[10]	Mohri, M., Rostamizadeh, A., Talwalkar, A. (2012) Foundations of machine learning. MIT press.
[11]	D. F. Andrews and C. L. Mallows (1974). Scale Mixtures of Normal Distributions. Journal of the Royal Statistical Society. Series B, 36, 99-102.
[12]	Mike West. (1987). On Scale Mixtures of Normal Distributions. Biometrika, 74, 646-648.
[13]	Yoonkyung Lee and Zhenhuan Cui (2006). Characterizing the Solution Path of Multicategory Support Vector Machines. Statistica Sinica , 16, 391-409.
[14]	Zhihua Zhang and Michael I. J ordan (2006). Bayesian Multicategory Support Vector Machines Proceedings of the Twenty-Second Conference Annual Conference on Uncertainty in Artificial Intelligence , 552-559.
[15]	Yoonkyung Lee, Yi Lin and Grace Wahba (2004). Multicategory Support Vector Machines Theory and Application to the Classification of Microarray Data and Satellite Radiance Data Journal of American Statistical Association, 99, 67-81.

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Yeqian Liu. (2019). Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines. International Journal of Data Science and Analysis, 5(3), 42-51. https://doi.org/10.11648/j.ijdsa.20190503.12

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Yeqian Liu. Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines. Int. J. Data Sci. Anal. 2019, 5(3), 42-51. doi: 10.11648/j.ijdsa.20190503.12

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Yeqian Liu. Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines. Int J Data Sci Anal. 2019;5(3):42-51. doi: 10.11648/j.ijdsa.20190503.12

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@article{10.11648/j.ijdsa.20190503.12,
  author = {Yeqian Liu},
  title = {Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {3},
  pages = {42-51},
  doi = {10.11648/j.ijdsa.20190503.12},
  url = {https://doi.org/10.11648/j.ijdsa.20190503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190503.12},
  abstract = {The support vector machine (SVM) has become very popular within the machine learning literature. Recently, SVM has received much attention from statisticians. It is well known that for multicategory classification problem, the commonly used multicategory SVM is based on the frequentist framework. In this paper, we develop a multi-class support vector machine under the Bayesian framework. Numerical studies were performed by EM and the Bayesian algorithm Gibbs sampler. Our results have shown that the classification accuracy of the Bayesian approach is comparable to that of frequentist approaches, while Bayesian approach also has the advantage of providing estimates of uncertainty in predictions.},
 year = {2019}
}

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TY  - JOUR
T1  - Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines
AU  - Yeqian Liu
Y1  - 2019/08/07
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190503.12
DO  - 10.11648/j.ijdsa.20190503.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 42
EP  - 51
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190503.12
AB  - The support vector machine (SVM) has become very popular within the machine learning literature. Recently, SVM has received much attention from statisticians. It is well known that for multicategory classification problem, the commonly used multicategory SVM is based on the frequentist framework. In this paper, we develop a multi-class support vector machine under the Bayesian framework. Numerical studies were performed by EM and the Bayesian algorithm Gibbs sampler. Our results have shown that the classification accuracy of the Bayesian approach is comparable to that of frequentist approaches, while Bayesian approach also has the advantage of providing estimates of uncertainty in predictions.
VL  - 5
IS  - 3
ER  -

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Author Information

Yeqian Liu

Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, USA

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Yeqian Liu. (2019). Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines. International Journal of Data Science and Analysis, 5(3), 42-51. https://doi.org/10.11648/j.ijdsa.20190503.12

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ACS Style

Yeqian Liu. Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines. Int. J. Data Sci. Anal. 2019, 5(3), 42-51. doi: 10.11648/j.ijdsa.20190503.12

Copy | Download

AMA Style

Yeqian Liu. Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines. Int J Data Sci Anal. 2019;5(3):42-51. doi: 10.11648/j.ijdsa.20190503.12

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@article{10.11648/j.ijdsa.20190503.12,
  author = {Yeqian Liu},
  title = {Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {3},
  pages = {42-51},
  doi = {10.11648/j.ijdsa.20190503.12},
  url = {https://doi.org/10.11648/j.ijdsa.20190503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190503.12},
  abstract = {The support vector machine (SVM) has become very popular within the machine learning literature. Recently, SVM has received much attention from statisticians. It is well known that for multicategory classification problem, the commonly used multicategory SVM is based on the frequentist framework. In this paper, we develop a multi-class support vector machine under the Bayesian framework. Numerical studies were performed by EM and the Bayesian algorithm Gibbs sampler. Our results have shown that the classification accuracy of the Bayesian approach is comparable to that of frequentist approaches, while Bayesian approach also has the advantage of providing estimates of uncertainty in predictions.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Data Augmentation and Bayesian Methods for Multicategory Support Vector Machines
AU  - Yeqian Liu
Y1  - 2019/08/07
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190503.12
DO  - 10.11648/j.ijdsa.20190503.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 42
EP  - 51
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190503.12
AB  - The support vector machine (SVM) has become very popular within the machine learning literature. Recently, SVM has received much attention from statisticians. It is well known that for multicategory classification problem, the commonly used multicategory SVM is based on the frequentist framework. In this paper, we develop a multi-class support vector machine under the Bayesian framework. Numerical studies were performed by EM and the Bayesian algorithm Gibbs sampler. Our results have shown that the classification accuracy of the Bayesian approach is comparable to that of frequentist approaches, while Bayesian approach also has the advantage of providing estimates of uncertainty in predictions.
VL  - 5
IS  - 3
ER  -

Copy | Download