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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.

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