ORIGINAL ARTICLE Multi-class motor imagery EEG classification using collaborative representation-based semi-supervised extreme learning machine Qingshan She 1 & Jie Zou 1 & Zhizeng Luo 1 & Thinh Nguyen 2 & Rihui Li 2 & Yingchun Zhang 2 Received: 17 December 2019 /Accepted: 6 July 2020 # International Federation for Medical and Biological Engineering 2020 Abstract Both labeled and unlabeled data have been widely used in electroencephalographic (EEG)-based brain-computer interface (BCI). However, labeled EEG samples are generally scarce and expensive to collect, while unlabeled samples are considered to be abundant in real applications. Although the semi-supervised learning (SSL) allows us to utilize both labeled and unlabeled data to improve the classification performance as against supervised algorithms, it has been reported that unlabeled data occasionally undermine the performance of SSL in some cases. To overcome this challenge, we propose a collaborative representation-based semi-supervised extreme learning machine (CR-SSELM) algorithm to evaluate the risk of unlabeled samples by a new safety- control mechanism. Specifically, the ELM model is firstly used to predict unlabeled samples and then the collaborative repre- sentation (CR) approach is employed to reconstruct the unlabeled samples according to the obtained prediction results, from which the risk degree of unlabeled sample is defined. A risk-based regularization term is then constructed accordingly and embedded into the objective function of the SS-ELM. Experiments conducted on benchmark and EEG datasets demonstrate that the proposed method outperforms the ELM and SS-ELM algorithm. Moreover, the proposed CR-SSELM even offers the best performance while SS-ELM yields worse performance compared with its supervised counterpart (ELM). Keywords Brain-computer interface . Multi-class motor imagery . Electroencephalogram . Semi-supervised extreme learning machine . Collaborative representation . Safety aware 1 Introduction The EEG-based brain-computer interface (BCI) is a kind of communication and control system that rely on neural electri- cal activity to help the motor-disabled people control extern devices [1]. Motor imagery (MI) is a typical paradigm in the EEG-based BCI research, where the mental imagination of movements is discriminated and translated into control com- mands without performing any muscle activity [2]. The clas- sification problem, which decodes various commands based on EEG-derived features, is considered to be a key focus in the area of MI-based BCI. As EEG signals generally suffer mul- tiple limitations, including low signal-to-noise ratio (SNR), non-stationarity, intra-subject variability, and several sources of interference and artifacts [3], it remains a challenging task for accurate and real-time classification of EEG signals. Also, the analysis of multi-class EEG signal is an urgent problem of BCI. In order to achieve effective classification of EEG signals, a number of machine learning algorithms have been increasingly proposed in recent years, mainly including linear discriminant analysis (LDA), neural networks (NN), support vector machines (SVM), nonlinear Bayesian classifiers, and nearest neighbor clas- sifiers [3–6]. Recently, the extreme learning machine (ELM) method proposed by Huang et al. [7, 8] has been rapidly employed as a supervised learning algorithm in the field due to its superior training speed and generalizability compared with traditional NN and SVM algorithms [9]. However, the perfor- mance of ELM algorithm heavily relies on large numbers of labeled samples; this algorithm became impractical in some cases due to the difficulty to acquire sufficient labeled samples in real- world. On the contrary, unlabeled samples are easy to collect and * Qingshan She qsshe@hdu.edu.cn * Yingchun Zhang yzhang94@uh.edu 1 Institute of Intelligent Control and Robotics, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, China 2 Department of Biomedical Engineering, University of Houston, Houston, TX 77204, USA Medical & Biological Engineering & Computing https://doi.org/10.1007/s11517-020-02227-4