Cross-Subject and Cross-Montage EEG Transfer Learning via Individual Tangent Space Alignment and Spatial-Riemannian Feature Fusion

Nicole Lai-Tan; Xiao Gu; Marios G. Philiastides; Fani Deligianni

Fig. 1: Diagram illustrating the proposed PS - ITSA. Training (yellow) and Testing (blue) signals are represented as ‘squares’, with corresponding covariance means as circles labelled with the metric used for calculation ( LE = Log-Euclidean). Aligned signals are depicted as ‘squares with curved corners’ and extracted features are displayed as ‘flattened’ rectangles. The PS can be categorised into three steps (1) Recentering (pink), (2) Rescale (orange) and (3) Rotation (green). During the supervised Rotation step, only the calibration subset is used to derive transformational parameters to rotate the evaluation subset. A 2-fold cross validation is also implemented to ensure both subsets serve as the calibration and evaluation once.

Fig. 2: Diagram illustrating the fusion of RCSP - Riemannian geometry features. Yellow outlines denote pre-PS steps and pink outlines represent steps that are part of the recentering step of ‘ITSA’. The keys are as follows: Orange square - EEG signals, Blue square - covariance matrices, Blue circle - CSP filter obtained using arithmetic, depicted by the ‘A’, Pink square - spatially filtered EEG signals, Purple square - Projected dataset onto the tangent space, Rectangular - extracted features in the form of taking log-variance.

Fig. 3: Sliding window

(s)

segmentation of signals. The top horizontal line represents the EEG signal with vertical ticks marking the onset of auditory cues (AC) denoted as

A

. We segment adaptive and non-adaptive ‘blocks’, defined as the first 3 adaptive ( red ) and middle ( blue ) AC and illustrate as the orange rectangle taken from the [

A_{x}-256

:

A_{x+2}+256

] of the adaptive condition. Windows of

s=100

are slid across the segment for our dataset to obtain EEG trials,

t

	Advance Tempo		Delay Tempo
	Baseline (No PS)	LOSO (‘ITSA’ - proposed PS)	Baseline (No PS)	LOSO (‘ITSA’ - proposed PS)
Seq. RCSP-Rie (%)	54.39 $\pm$ 11.05 (CI: 48.90 - 59.88)	61.15 $\pm$ 7.27 (CI: 57.54 - 64.77) (*)	41.96 $\pm$ 18.10 (CI: 32.96 - 50.97)	57.28 $\pm$ 5.65 (CI: 54.47 - 60.09) () (*)
Par. RCSP-Rie (%)	56.23 $\pm$ 8.43 (CI: 52.03 - 60.42)	61.34 $\pm$ 5.49 (CI: 58.60 - 64.07) () (*)	42.65 $\pm$ 19.52 (CI: 32.94 - 52.36)	58.52 $\pm$ 5.65 (CI: 55.71 - 61.33) () (*)

TABLE I: Averaged F1-scores and standard deviation across testing subjects and standard deviations for classification of Advance and Delay Tempo features comparing the baseline (without PS) and our proposed ‘ITSA’. Metrics are reported for the two feature extraction approaches: Seq. RCSP-Rie and Par. RCSP-Rie. 95% confidence intervals are also provided. Statistically significant improvements resulting from the PS (uncorrected

p<0.05

are denoted by (*) , corrected

p<0.0167

using Bonferroni-correction are denoted by (**) ).

	recentering (per subject)	Rescaling Step	Rotation Step
Baseline (w/out PS)
‘Adaptive M’ [ 17 ]	✓
‘TS’ [ 18 ]		✓	✓
‘ITSA’ - proposed method	✓	✓	✓

TABLE II: Ablation table on pre-alignment strategies. Checkmarks indicate the presence of the component in pre-alignment strategy.

Advance Tempo
	LOSO (‘Adaptive M’) [ 17 ]	LOSO (‘TS’) [ 18 ]	LOSO (‘ITSA’ - proposed PS)
Seq. RCSP-Rie (%)	57.44 $\pm$ 5.35 (CI: 54.78 - 60.10)	60.99 $\pm$ 6.41 (CI: 57.80 - 64.18) (*)	61.15 $\pm$ 7.27 (CI: 57.54 - 64.77) (*)
Par. RCSP-Rie (%)	59.29 $\pm$ 4.13 (CI: 57.24 - 61.35)	61.00 $\pm$ 5.63 (CI: 58.21 - 63.80) (*)	61.34 $\pm$ 5.49 (CI: 58.60 - 64.07) () (*)
Delay Tempo
	LOSO (‘Adaptive M’) [ 17 ]	LOSO (‘TS’) [ 18 ]	LOSO (‘ITSA’ - proposed PS)
Seq. RCSP-Rie (%)	56.38 $\pm$ 6.41 (CI: 59.50-63.19) () (*)	57.13 $\pm$ 5.50 (CI: 54.40 - 59.87) () (*)	57.28 $\pm$ 5.65 (CI: 54.47 - 60.09) () (*)

TABLE III: Averaged F1-scores and standard deviations across testing subjects for classification of Advance and Delay Tempo features from our LOSO-CV ablation study. We compared our proposed PS (‘ITSA’) with two PS baselines - ‘Adaptive M’ [ 17 ] and ‘TS’ [ 18 ] . Metrics are reported for the two feature extraction methods: Seq. RCSP-Rie and Par. RCSP-Rie. 95% confidence intervals are also provided. Statistically significant improvement from the implementation of PS method (uncorrected

p<0.05

are denoted by (*) , corrected

p<0.0167

using Bonferroni-correction are denoted by (**) ).

Fig. 4: Box plot displaying the distribution of F1 score across 18 testing subjects and pre-alignment strategies during our LOSO-CV. Each box represents the interquartile range (25 and 75th percentiles) with the central line indicating the median. Whiskers extend to the most extreme points not considered to be outliers. Outliers are represented by ‘o’ markers. We compared our proposed PS (‘ITSA’) with two PS baselines - ‘Adaptive M’ [ 17 ] and ‘TS’ [ 18 ] . Metrics are reported for the two feature extraction methods: Seq. RCSP-Rie (blue) and Par. RCSP-Rie (red) and across the temporal conditions ‘Advance’ and ‘Delay Tempo’.

Fig. 5: Comparisons of testing subjects where ‘Adaptive M’ , ‘TS’ and ‘ITSA’ PS enhanced or preserved classification performance with ‘Seq. RCSP-Rie’ and ‘Par. RCSP-Rie’. The testing subject is denoted in the first column, with the first two rows categorised as ‘successful’ (subjects 1 and 18) and the bottom two as ‘unsuccessful’ (subjects 3 and 13). Respective F1 scores (%) for each testing subject and applied PS are displayed beneath the t-SNE plot. The highest performing PS are highlighted in yellow, with the second highest in orange. For ‘TS’ and ‘ITSA’ PS, corresponding t-SNE projections and F1 scores are reported using the ‘Fold 1’ features of the PS calibration-testing used in the ‘Rotation’ step.

Fig. 6: t-SNE projections (n components = 3, perplexity = 5) to visualise Riemannian distance between each subject’s centre and the alignment reference point (identity matrix - X ). Testing subjects of interest are displayed by blue (subject 3) and green (subject 13) squares, while successful testing subjects are displayed by purple (subject 1) and orange (subject 18) circles. The remaining subjects that create the training dataset are shown as red circles. Here, each sample corresponds to a subject-specific covariance representation, resulting in a total of

N=18

samples.

Fig. 7: LOSO classification performances for cross-montage experiment. Simulation of testing datasets using 61 and 19 electrodes (10-10 and 10-20 montage) was tested on the trained model with 108 electrodes. Comparisons between baseline performance ( blue ) and after implementation of proposed ‘ITSA’ ( green ) are depicted. Shaded areas denote the corresponding standard deviations across leave-one-subject-out folds (i.e., across held-out test subjects).

Fig. 8: Performance curves showing the relationship between the training size (number of subjects

N_{\text{train}}

) and averaged (black) LOSO-CV performance for test subject 1 ( red ), 3 ( blue ), 6 ( green ), 10 ( cyan ), 14 ( magenta ) and 18 ( orange ) as testing subjects for (a) Advance and (b) Delay tempo. Observed F1 scores (crosses) are reported for

N_{\text{train}}=5,9,15,17

. Predicted F1 scores (solid dots) for a logarithmic (dash-dotted) and linear (dotted) fit are displayed. Baselines, without ITSA (grey dashed), are obtained as the averaged F1 score across all testing subjects,

N_{\text{train}}=17

.

Advance Tempo
	Within-subject	Cross-subject	LOSO (w/out PS)	LOSO (‘ITSA’ - proposed )
Seq. RCSP-Rie (%)	94.18	68.17	54.39	61.15
Par. RCSP-Rie (%)	87.95	69.64	56.23	61.34
Delay Tempo
	Within-subject	Cross-subject	LOSO (w/out PS)	LOSO (‘ITSA’ - proposed )
Seq. RCSP-Rie (%)	94.33	69.96	41.96	57.28

TABLE IV: F1-scores (%) for classification of Tempo Advance and Tempo Delay features from within-subject, cross-subject, and LOSO splits. Metrics are reported for two fusion methods: Seq. RCSP-Rie and Par. RCSP-Rie.

Nicole Lai-Tan is currently a PhD student in the Social AI CDT at the University of Glasgow, funded by UKRI. She holds a MSc in Mathematics and a BSc in Mathematics and Music from the University of Leeds. Her research interest includes the development of AI algorithms to understand neurophysiological data with relation to gait dysfunction and its application within music therapy to support motor and cognitive rehabilitation.

Table 13

Dr. Xiao Gu is a Senior Research Associate at the Computation Health Informatics (CHI) Lab, Department of Engineering Science at the University of Oxford. He holds a PhD degree in Computing and MRes degree (Distinction & Dean’s Prize) in Medical Robotics and Image Guided Intervention from Imperial College London in 2023 and 2019 respectively. His research focuses on integrating pervasive sensing and deep learning for healthcare, to address pressing generalisation issues in real-world applications.

Table 14

Professor. Marios G. Philiastides is a Professor at the School of Psychology and Neuroscience and Director of the Centre for Cognitive Neuroimaging at the University of Glasgow. He received his doctoral degree in Biomedical Engineering from Columbia University and MSc in Electrical Engineering from Stanford University. His research focuses on multimodal neuroimaging and computational modelling of human decision making and learning in health and disease.

Table 15

Dr. Fani Deligianni is a Senior Lecturer at the School of Computing Science at the University of Glasgow. She holds a PhD in Medical Image Computing (Imperial College London), an MSc in Advanced Computing (Imperial College London), an MSc in Neuroscience (University College London) and a MEng (equivalent) in Electrical and Computer Engineering (Aristotle University, Greece). Her research interest involves developing machine learning methods for the analysis of medical images, neurophysiological data and human motion while preserving the privacy or the users.

Table 16

TABLE V: F1 scores (%) for each testing subject in LOSO-CV classification - Advance Tempo. Highest performing score for each subject is highlighted in green.

TABLE VIII: F1 scores (%) for each testing subject in LOSO-CV classification - Delay Tempo. Highest performing score for each subject is highlighted in green.

	SVM hyperparameter tune				RF
	0.01	0.1	1	10
Without PS	56.65 $\pm$ 3.29	61.68 $\pm$ 6.95	61.67 $\pm$ 7. 54	59.80 $\pm$ 9.32	49.39 $\pm$ 13.72
With ITSA	61.84 $\pm$ 6.81	66.84 $\pm$ 6.81	66.79 $\pm$ 3.64	63.15 $\pm$ 6.46	62.97 $\pm$ 6.39

TABLE XI: Averaged F1 scores for hyperparameter tuned SVM and Random Forest classification on LOSO validation using testing subjects 6, 11 and 18 with ‘Par. RCSP-Rie’ feature extraction in the ‘Advance Tempo’. F1 scores with highest performing parameters are denoted in green.

Fig. 9: Confusion matrix across temporal conditions ‘Advance’ and ‘Delay Tempo’ and feature extraction methods ‘Seq.’ and ‘Par. RCSP-Rie’ comparing Baseline - unaligned features and proposed ‘ITSA’ implementation.

Fig. 10: AUROC plots across temporal conditions ‘Advance’ and ‘Delay Tempo’ and feature extraction methods ‘Seq.’ and ‘Par. RCSP-Rie’ comparing Baseline - unaligned features (blue, dashed) and proposed ‘ITSA’ implementation (orange)

Fig. 11: PR-AUC plots across temporal conditions ‘Advance’ and ‘Delay Tempo’ and feature extraction methods ‘Seq.’ and ‘Par. RCSP-Rie’ comparing Baseline - unaligned features (blue, dashed) and proposed ‘ITSA’ implementation (orange)

Temporal condition	Feature	Friedman $\chi^{2}$ (2)	Friedman $p$	Post-hoc Wilcoxon comparisons
Advance Tempo	Seq. RCSP-Rie	10.732	0.0047	Adaptive M vs. TS: 0.0347 () $\rightarrow$ 0.1040 Adaptive M vs. ITSA: 0.0386 () $\rightarrow$ 0.1040 TS vs. ITSA: 0.0552 $\rightarrow$ 0.1040
	Par. RCSP-Rie	5.324	0.0698	Adaptive M vs. TS: 0.0936 $\rightarrow$ 0.1284 Adaptive M vs. ITSA: 0.0642 $\rightarrow$ 0.1284 TS vs. ITSA: 0.0075 () $\rightarrow$ 0.0224 (*)
Delay Tempo	Seq. RCSP-Rie	0.457	0.7957	Adaptive M vs. TS: 0.9479 $\rightarrow$ 1.0000 Adaptive M vs. ITSA: 0.9133 $\rightarrow$ 1.0000 TS vs. ITSA: 0.2775 $\rightarrow$ 0.8326
	Par. RCSP-Rie	2.056	0.3577	Adaptive M vs. TS: 0.3491 $\rightarrow$ 0.6543 Adaptive M vs. ITSA: 0.3271 $\rightarrow$ 0.6543 TS vs. ITSA: 0.1024 $\rightarrow$ 0.3073

TABLE XII: Statistical comparison of F1-score performance across temporal conditions and feature extraction methods. Values in the post-hoc column are reported as raw

p

-value

\rightarrow

Holm-adjusted

p

-value. The Friedman

p

-value represents the omnibus test across Adaptive M, TS, and ITSA. Post-hoc comparisons were performed using Wilcoxon signed-rank tests, with the raw

p

-value

\rightarrow

Holm-adjusted

p

-value, with Holm correction reported across the three pairwise comparisons within each condition. Uncorrected

p<0.05

are denoted by (*) and (**) indicate

p<0.05

after Holm correction.

Advance Tempo
	Baseline (No PS)	‘ITSA’ (25% calibration)	‘ITSA’ (50% calibration)
Seq. RCSP-Rie (%)	54.39 $\pm$ 11.05 (CI: 48.90 - 59.88)	58.75 $\pm$ 8.40 (CI: 55.27- 62.21)	61.15 $\pm$ 7.27 (CI: 57.54 - 64.77) (*)
Par. RCSP-Rie (%)	56.23 $\pm$ 8.43 (CI: 52.03 - 60.42)	59.57 $\pm$ 5.02 (CI: 57.07 - 62.07)	61.34 $\pm$ 5.49 (CI: 58.60 - 64.07) () (*)
Delay Tempo
	Baseline (No PS)	‘ITSA’ (25% calibration)	‘ITSA’ (50% calibration)
Seq. RCSP-Rie (%)	41.96 $\pm$ 18.10 (CI: 32.96 - 50.97)	54.59 $\pm$ 5.89 (CI: 51.66 - 57.51) () (*)	57.28 $\pm$ 5.65 (CI: 54.47 - 60.09) () (*)

TABLE XIII: Averaged F1-scores and standard deviations across testing subjects for classification of Advance and Delay Tempo features from our LOSO-CV ablation study. We compared calibration subset (allocating 25% and 50% of testing features to our calibration subset) during our Rotation step of the proposed ‘ITSA’ against baseline, unaligned features. Metrics are reported for the two feature extraction methods: Seq. RCSP-Rie and Par. RCSP-Rie. 95% confidence intervals are also provided. Statistically significant improvement from the implementation of PS method (uncorrected

p<0.05

are denoted by (*) , corrected

p<0.0167

using Bonferroni-correction are denoted by (**) ).

Fig. 12: Average variation in trial counts across training subjects for each

N_{train}

across the temporal conditions ‘ Advance Tempo ’ (orange) and ‘ Delay Tempo ’ (blue). Error bars represent the variability across testing subjects (1, 3, and 18), and percentages for each marker indicate the proportion of overall mean trial count.

Fig. 13: Performance curve illustrating the relationship between the classification performance (F1 score) and the percentage of features retained after application of PCA feature reduction. Averaged results are shown from a LOSO-CV for three configurations: (1) without the use of ‘ITSA’ (‘W/out ITSA’ - blue), (2) ITSA-aligned features with feature reduction applied at the end of the preprocessing pipeline (‘W/ITSA - end of pipeline’ - green) and (3) ITSA-aligned features with feature reduction applied during the ‘rescaling’ step (‘W/ITSA - Rescale step’ - red). Standard deviations are depicted by the shaded area, and respective upper and lower boundaries are displayed with dashed lines.

Fig. 14: Signal-to-noise ratio (SNR) across testing subjects 1, 6 and 12 for 10-20, 10-10 and full 108-electrode configurations in the Delay Tempo using both ‘Seq’. and ‘Par. RCSP-Rie’. Subject-wise and averaged SNR are presented

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