Diffusion Inverse Filtering: Enhancing Functional Connectivity-Based Pattern Recognition by Counteracting Spatial Smoothing

Background/Objectives: This study proposes Diffusion Inverse Filtering (DIF), a spatially informed transformation designed to counteract spatial smoothing in functional-connectivity representations (i.e., functional networks) and thereby enhance their discriminative power for pattern recognition. Spatial smoothing in electroencephalography (EEG) signals and derived features, such as functional connectivity, is largely attributed to volume conduction. Functional connectivity has been increasingly used in brain–computer interface (BCI) studies; however, this spatial smoothing can introduce spurious connections and distort functional-connectivity patterns. Methods: DIF approximates spatial smoothing in functional connectivity, which is potentially associated with volume conduction, as a diffusion-like process and applies a regularized inverse operation to transform the observed functional networks into networks with enhanced discriminative representations. The effectiveness of DIF in enhancing the discriminative power of functional-connectivity representations in pattern recognition was evaluated using emotion recognition as the paradigm task, which is a critical component of BCI systems. Experimental results show that DIF generally improves emotion-recognition performance relative to the originally observed functional networks under electrode-sparsification conditions, with the most consistent improvements observed for Pearson correlation coefficient (PCC) estimation. Both signal-level processing, which operates on EEG signals before functional-connectivity estimation, and function-al-connectivity-level transformations, including graph signal processing (GSP)-based filtering applied after functional-connectivity estimation, were included as comparators. Under this framework, DIF is also considered a functional-connectivity-level transformation, but does not rely on a GSP framework. Results: The performance of DIF demonstrates the potential of functional-connectivity-level transformation as a complement or alternative to signal-level processing for enhancing connectivity-based pattern recognition. Overall, DIF improves classification performance and offers strong compatibility with modern functional-connectivity-based BCI pipelines.