Large-scale robust transductive support vector machines

Çevikalp, Hakan; Franc, Vojtĕch

doi:10.1016/j.neucom.2017.01.012

Cited by 26 publications

(20 citation statements)

References 28 publications

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“…Thus, H 1 (| t |) was replaced by exp(−3 t 2 ) in the LDS method [25]. However, most TSVM methods employed a symmetric ramp loss function for unlabelled samples [20, 21].…”

Section: Methodsmentioning

confidence: 99%

“…Many TSVM methods follow this idea in LDS [20, 21, 24]. However, one problem is that the distribution of a limited labelled set cannot always represent that of a large unlabelled set, especially when the existing labelled set is unbalanced.…”

Section: Methodsmentioning

confidence: 99%

“…In CCCP, the balancing constraint in equation (8) can be applied to the minimization problem by introducing an extra sample ( x 0 =(1/ U )∑ i = L +1 L + U ( x i ), y 0 =1) and a variable ( ζ 0 =(1/ L ) ∑ i =1 L y i ) [20, 21].…”

Section: Methodsmentioning

confidence: 99%

“…However, CCCP could not scale well with larger datasets. Robust TSVM (RTSVM) provided higher computational efficiency for millions of samples by using the stochastic gradient (SG) method to solve the primal optimization problem [21]. Due to insufficient domain knowledge, it remains challenging for the TSVM model to provide high accuracy when used with obscure unlabelled data [22].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, it may be unreasonable to preset the ratio of positive to negative samples in the unlabelled set to be equal to the ratio in the labelled set in many TSVM methods [20, 21, 24, 25], especially when the small labelled set is extremely unbalanced. Incorrect estimation of this ratio may decrease the classification accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Improved Transductive Support Vector Machine for a Small Labelled Set in Motor Imagery-Based Brain-Computer Interface

Hua

Zhang

et al. 2019

Computational Intelligence and Neuroscience

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Long and tedious calibration time hinders the development of motor imagery- (MI-) based brain-computer interface (BCI). To tackle this problem, we use a limited labelled set and a relatively large unlabelled set from the same subject for training based on the transductive support vector machine (TSVM) framework. We first introduce an improved TSVM (ITSVM) method, in which a comprehensive feature of each sample consists of its common spatial patterns (CSP) feature and its geometric feature. Moreover, we use the concave-convex procedure (CCCP) to solve the optimization problem of TSVM under a new balancing constraint that can address the unknown distribution of the unlabelled set by considering various possible distributions. In addition, we propose an improved self-training TSVM (IST-TSVM) method that can iteratively perform CSP feature extraction and ITSVM classification using an expanded labelled set. Extensive experimental results on dataset IV-a from BCI competition III and dataset II-a from BCI competition IV show that our algorithms outperform the other competing algorithms, where the sizes and distributions of the labelled sets are variable. In particular, IST-TSVM provides average accuracies of 63.25% and 69.43% with the abovementioned two datasets, respectively, where only four positive labelled samples and sixteen negative labelled samples are used. Therefore, our algorithms can provide an alternative way to reduce the calibration time.

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“…Thus, H 1 (| t |) was replaced by exp(−3 t 2 ) in the LDS method [25]. However, most TSVM methods employed a symmetric ramp loss function for unlabelled samples [20, 21].…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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