Robust Support Vector Regression for Uncertain Input and Output Data

The increasing demands of location-based services have spurred the rapid development of indoor positioning system and indoor localization system interchangeably (IPSs). However, the performance of IPSs suffers from noisy measurements. In this paper, two kinds of robust extreme learning machines (RELMs), corresponding to the close-to-mean constraint, and the small-residual constraint, have been proposed to address the issue of noisy measurements in IPSs. Based on whether the feature mapping in extreme learning machine is explicit, we respectively provide random-hidden-nodes and kernelized formulations of RELMs by second order cone programming. Furthermore, the computation of the covariance in feature space is discussed. Simulations and real-world indoor localization experiments are extensively carried out and the results demonstrate that the proposed algorithms can not only improve the accuracy and repeatability, but also reduce the deviation and worst case error of IPSs compared with other baseline algorithms.

show abstract

“…It follows from [25] and [26] that, by inserting CTM and SR constraints into SVR, the predictions can be robust to perturbations in the data set.…”

Section: A Uncertainties Of Input and Output Datamentioning

confidence: 99%

Robust Extreme Learning Machine With its Application to Indoor Positioning

Zou

Zhou

et al. 2016

IEEE Trans. Cybern.

101

View full text Add to dashboard Cite

show abstract

“…This has been explored to some extent by previous authors, though in many cases uncertainties are only treated for the either inputs or the outputs; not both [25,10,9]. In some instances both uncertainties were simultaneously considered, however the algorithm was treated in the dual form [8]. As has been previously discussed, this can quickly become cumbersome when dealing with large datasets.…”

Section: Support Vector Machinesmentioning

confidence: 99%

“…Therefore, the focus of this paper is on the development of an SVM algorithm for the handling of uncertainty in both the data and the training labels. Recently this problem has received some attention [8,9,10], though all seem to treat the SVM in its dual form and make various assumptions about the uncertainties. The formulation presented in this paper is general and loosely based on Total Least Squares [11,12] and recasts the primal SVM objective function to incorporate uncertainties into the optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Data mining for real mining: A robust algorithm for prospectivity mapping with uncertainties

Granek

Haber

2015

Proceedings of the 2015 SIAM International Conference on Data Mining

View full text Add to dashboard Cite

Mineral prospectivity mapping is an emerging application for machine learning algorithms which presents a series of practical difficulties. The goal is to learn the mapping function which can predict the existence or absence of economic mineralization from a compilation of geoscience datasets (ie: bedrock type, magnetic signature, geochemical response etc). The challenges include sparse, imbalanced labels (mineralization occurrences), varied label reliability, and a wide range in data quality and uncertainty. In order to address these issues an algorithm was developed based on total least squares and support vector machine regression which incorporates both data and label uncertainty into the objective function. This was done without losing sparsity in the residuals, thus maintaining minimal support vectors.Mineral prospectivity mapping is an application for machine learning which presents a series of practical difficulties. The goal is to learn the mapping function which can predict the existence of mineralization from a compilation of geoscience datasets. Challenges include sparse, imbalanced labels, varied label reliability, and a wide range in data uncertainty. To address this, an algorithm was developed based on TLS and SVM which incorporates both data and label uncertainty into the objective function.

show abstract

“…However, as shown in [22], the classical regularized support vector machine has a close connection with its robust formulation. Robust optimization [23], [24] has found wide applications in support vector classification [25]- [32] and support vector regression [33], [34]. Two frameworks have been proposed for the worst case CVaR optimization in portfolio theory.…”

Section: Introductionmentioning

confidence: 99%

Robust Novelty Detection via Worst Case CVaR Minimization

Wang

Dang

Wang

2015

IEEE Trans. Neural Netw. Learning Syst.

View full text Add to dashboard Cite

Novelty detection models aim to find the minimum volume set covering a given probability mass. This paper proposes a robust single-class support vector machine (SSVM) for novelty detection, which is mainly based on the worst case conditional value-at-risk minimization. By assuming that every input is subject to an uncertainty with a specified symmetric support, this robust formulation results in a maximization term that is similar to the regularization term in the classical SSVM. When the uncertainty set is l1 -norm, l∞ -norm or box, its training can be reformulated to a linear program; while the uncertainty set is l2 -norm or ellipsoidal, its training is a tractable second-order cone program. The proposed method has a nice consistent statistical property. As the training size goes to infinity, the estimated normal region converges to the true provided that the magnitude of the uncertainty set decreases in a systematic way. The experimental results on three data sets clearly demonstrate its superiority over three benchmark models.

show abstract

Robust Support Vector Regression for Uncertain Input and Output Data

Cited by 46 publications

References 33 publications

Robust Extreme Learning Machine With its Application to Indoor Positioning

Robust Extreme Learning Machine With its Application to Indoor Positioning

Data mining for real mining: A robust algorithm for prospectivity mapping with uncertainties

Robust Novelty Detection via Worst Case CVaR Minimization

Contact Info

Product

Resources

About