A major challenge in EEG-based brain-computer interfaces (BCIs) is the intersession nonstationarity in the EEG data that often leads to deteriorated BCI performances. To address this issue, this letter proposes a novel data space adaptation technique, EEG data space adaptation (EEG-DSA), to linearly transform the EEG data from the target space (evaluation session), such that the distribution difference to the source space (training session) is minimized. Using the Kullback-Leibler (KL) divergence criterion, we propose two versions of the EEG-DSA algorithm: the supervised version, when labeled data are available in the evaluation session, and the unsupervised version, when labeled data are not available. The performance of the proposed EEG-DSA algorithm is evaluated on the publicly available BCI Competition IV data set IIa and a data set recorded from 16 subjects performing motor imagery tasks on different days. The results show that the proposed EEG-DSA algorithm in both the supervised and unsupervised versions significantly outperforms the results without adaptation in terms of classification accuracy. The results also show that for subjects with poor BCI performances when no adaptation is applied, the proposed EEG-DSA algorithm in both the supervised and unsupervised versions significantly outperforms the unsupervised bias adaptation algorithm (PMean).

There are two important issues in neuro-fuzzy modeling: (1) interpretability—the ability to describe the behavior of the system in an interpretable way—and (2) accuracy—the ability to approximate the outcome of the system accurately. As these two objectives usually exert contradictory requirements on the neuro-fuzzy model, certain compromise has to be undertaken. This letter proposes a novel rule reduction algorithm, namely, Hebb rule reduction, and an iterative tuning process to balance interpretability and accuracy. The Hebb rule reduction algorithm uses Hebbian ordering, which represents the degree of coverage of the samples by the rule, as an importance measure of each rule to merge the membership functions and hence reduces the number of the rules. Similar membership functions (MFs) are merged by a specified similarity measure in an order of Hebbian importance, and the resultant equivalent rules are deleted from the rule base. The rule with a higher Hebbian importance will be retained among a set of rules. The MFs are tuned through the least mean square (LMS) algorithm to reduce the modeling error. The tuning of the MFs and the reduction of the rules proceed iteratively to achieve a balance between interpretability and accuracy. Three published data sets by Nakanishi (Nakanishi, Turksen, & Sugeno, 1993), the Pat synthetic data set (Pal, Mitra, & Mitra, 2003), and the traffic flow density prediction data set are used as benchmarks to demonstrate the effectiveness of the proposed method. Good interpretability, as well as high modeling accuracy, are derivable simultaneously and are suitably benchmarked against other well-established neuro-fuzzy models.

System modeling with neuro-fuzzy systems involves two contradictory requirements: interpretability verses accuracy. The pseudo outer-product (POP) rule identification algorithm used in the family of pseudo outer-product-based fuzzy neural networks (POPFNN) suffered from an exponential increase in the number of identified fuzzy rules and computational complexity arising from high-dimensional data. This decreases the interpretability of the POPFNN in linguistic fuzzy modeling. This article proposes a novel rough set–based pseudo outer-product (RSPOP) algorithm that integrates the sound concept of knowledge reduction from rough set theory with the POP algorithm. The proposed algorithm not only performs feature selection through the reduction of attributes but also extends the reduction to rules without redundant attributes. As many possible reducts exist in a given rule set, an objective measure is developed for POPFNN to correctly identify the reducts that improve the inferred consequence. Experimental results are presented using published data sets and real-world application involving highway traffic flow prediction to evaluate the effectiveness of using the proposed algorithm to identify fuzzy rules in the POPFNN using compositional rule of inference and singleton fuzzifier (POPFNN-CRI(S)) architecture. Results showed that the proposed rough set–based pseudo outer-product algorithm reduces computational complexity, improves the interpretability of neuro-fuzzy systems by identifying significantly fewer fuzzy rules, and improves the accuracy of the POPFNN.