*Article* **Kernel-Based Phase Transfer Entropy with Enhanced Feature Relevance Analysis for Brain Computer Interfaces**

**Iván De La Pava Panche 1,\*, Andrés Álvarez-Meza 2, Paula Marcela Herrera Gómez 3, David Cárdenas-Peña 1, Jorge Iván Ríos Patiño <sup>1</sup> and Álvaro Orozco-Gutiérrez <sup>1</sup>**


**Abstract:** Neural oscillations are present in the brain at different spatial and temporal scales, and they are linked to several cognitive functions. Furthermore, the information carried by their phases is fundamental for the coordination of anatomically distributed processing in the brain. The concept of phase transfer entropy refers to an information theory-based measure of directed connectivity among neural oscillations that allows studying such distributed processes. Phase TE is commonly obtained from probability estimations carried out over data from multiple trials, which bars its use as a characterization strategy in brain–computer interfaces. In this work, we propose a novel methodology to estimate TE between single pairs of instantaneous phase time series. Our approach combines a kernel-based TE estimator defined in terms of Renyi's *α* entropy, which sidesteps the need for probability distribution computation with phase time series obtained by complex filtering the neural signals. Besides, a kernel-alignment-based relevance analysis is added to highlight relevant features from effective connectivity-based representation supporting further classification stages in EEG-based brain–computer interface systems. Our proposal is tested on simulated coupled data and two publicly available databases containing EEG signals recorded under motor imagery and visual working memory paradigms. Attained results demonstrate how the introduced effective connectivity succeeds in detecting the interactions present in the data for the former, with statistically significant results around the frequencies of interest. It also reflects differences in coupling strength, is robust to realistic noise and signal mixing levels, and captures bidirectional interactions of localized frequency content. Obtained results for the motor imagery and working memory databases show that our approach, combined with the relevance analysis strategy, codes discriminant spatial and frequencydependent patterns for the different conditions in each experimental paradigm, with classification performances that do well in comparison with those of alternative methods of similar nature.

**Keywords:** transfer entropy; kernel methods; Renyi's entropy; connectivity analysis; phase interactions
