Preserving Harmonic Structure in FPVS-Oddball: A Two-Dimensional Cluster-Based Permutation Approach.

The fast periodic visual stimulation oddball paradigm (FPVS-oddball), which combines multi-input frequency tagging with an oddball design, is a powerful electroencephalography (EEG) technique for probing cognitive function. Traditionally, FPVS-oddball analysis collapses steady-state responses across harmonics into composite measures, which improves response detection but discards valuable information about the harmonic composition of responses. Here, we apply a two-dimensional (sensor × harmonic) permutation test, incorporating a novel free harmonic clustering procedure that allows clustering across sensors and harmonics, thereby preserving harmonic-related information. Using datasets on object recognition (real vs. pseudo-objects) and line orientation discrimination, we show that the two-dimensional approach detects condition-specific differences in the spatial and harmonic distribution of responses that are missed by a one-dimensional (sensor-only) test of composite responses. For object recognition, real objects elicited stronger left- and right-lateralised oddball responses at higher harmonics, consistent with additional semantic processing. For orientation discrimination, large versus small deviations elicited distinct harmonic-specific activation patterns, reflecting qualitatively different processing. These results demonstrate that two-dimensional cluster-based permutation testing provides sensitivity to the spatial and harmonic distribution of FPVS-oddball responses.