A Trace Lasso Regularized Robust Nonparallel Proximal Support Vector Machine for Noisy Classification

Generalized eigenvalue proximal support vector machine (GEPSVM) and its improvement IGEPSVM are excellent nonparallel classification methods due to their excellent generalization. However, all of them adopt the square L_{2} -norm metric to implement their empirical risk or penalty, which is sensiti...

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Bibliographic Details
Published in:IEEE access 2019, Vol.7, p.47171-47184
Main Authors: Chen, Wei-Jie, Yang, Kai-Li, Shao, Yuan-Hai, Chen, Yu-Juan, Zhang, Ju, Yao, Jing-Jing
Format: Article
Language:English
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Classification
classification algorithms
Cognitive tasks
Correlation
Dispersion
Eigenvalues
Eigenvalues and eigenfunctions
Iterative algorithms
Noise measurement
Noise sensitivity
Optimization
Outliers (statistics)
regularization
Robustness
Support vector machines
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Summary:Generalized eigenvalue proximal support vector machine (GEPSVM) and its improvement IGEPSVM are excellent nonparallel classification methods due to their excellent generalization. However, all of them adopt the square L_{2} -norm metric to implement their empirical risk or penalty, which is sensitive to noise and outliers. Moreover, in many real-world learning tasks, it is a significant challenge for GEPSVMs when the data appears highly correlated. To alleviate the above issues, in this paper, we propose a novel trace lasso regularized robust nonparallel proximal support vector machine (RNPSVM) for noisy classification. Compared with GEPSVMs, our RNPSVM enjoys the following advantages. First, the empirical risk of RNPSVM is implemented by the robust L_{1} -norm metric with a maximum margin criterion. Namely, it aims to maximize the L_{1} -norm inter-class distance dispersion while minimizing the L_{1} -norm intra-class distance dispersion simultaneously. Second, to capture the sparsity and the underlying correlation of data, a trace lasso (adaptive norm-based training data) is further introduced to regularize RNPSVM. Third, an iterative algorithm is designed to solve the maximization optimization problem of RNPSVM, whose convergence is guaranteed theoretically. The extensive experimental results on both synthetic and real-world noisy datasets demonstrate the effectiveness of RNPSVM.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2019.2893531