Binary and multi-class motor imagery using Renyi entropy for feature extraction

Entropy, the complexity measures for time series, has found numerous successful applications in brain signal analysis such as detection of epileptic seizure and monitoring the depth of anesthesia. Renyi entropy generalizes the well-known Shannon entropy, and hence providing better flexibility in application to real data. The objective of this paper is to evaluate the effectiveness of Renyi entropy as feature extraction method for motor imagery (MI)-based brain-computer interface (BCI). In this paper, Renyi entropy has been implemented in MI systems of various settings using BCI competition data sets. The classification accuracy of Renyi entropy in all data sets is benchmarked against common spatial pattern (CSP), the state-of-the-art feature extraction method. For common binary class data sets, Renyi entropy achieves an accuracy of approximately 3.4 % higher for BCI Competition II Data Set III and 0.87 % lower for BCI Competition III Data Set I, and there is no difference in accuracy for BCI Competition III Data Set IVc when compared against conventional CSP. In small sample setting, the average classification accuracy using Renyi entropy is approximately 3.4 and 0.3 % higher as compared to conventional CSP and best performing variant of regularized CSP, respectively. In addition, Renyi entropy is also compared to other chaos-inspired feature extraction methods, namely Katz and Higuchi which are implemented for MI systems by earlier researchers. The effect of implementing Renyi entropy on multiple narrower frequency sub-bands is also investigated in this study. In multi-class setting, Renyi entropy shows no statistical difference (p = 0.6022, paired t test) in accuracy when compared to the algorithm of the BCI competition winner. However, Renyi entropy has an advantage of requiring only one single application of feature extraction regardless of the number of classes, while multiple implementation of CSP is required as CSP is originally designed for binary class problem. The successful application of Renyi entropy in all the aforementioned settings indicates that Renyi entropy is a viable feature extraction alternative for MI-based BCI systems.