Comparative evaluation of O2PLS and optimization-based methods for identifying shared and exclusive neural subspaces
Francesco E. Vaccari*1, Stefano Diomedi2, Matteo Filippini1, Marina De Vitis1, Patrizia Fattori1 1 Department of Biomedical and Neuromotor Sciences, University of Bologna, Bologna, Italy
2 Institute of Cognitive Sciences and Technologies, National Research Council, Padova
*Email: francesco.vaccari6@unibo.it
IntroductionNew techniques in Neuroscience allow the recording from hundreds of neurons across multiple brain regions. However, a key issue is disentangling the population dynamics shared across areas from those exclusive to each region. This study introduces two approaches that, to our best knowledge, were not used to analyze neural data before: O2PLS [1], a Partial Least Squares (PLS) regression extension that explicitly model shared and unique subspaces, and an optimization approach based on MANOPT toolbox to minimize an appropriate cost function [1]. We assess their performance in retrieving in latent dynamics in a simulated dataset and highlight trade-offs in accuracy and computational load. Methods Synthetic data were generated with known latent shared and exclusive variables (similar to [3]). Many simulation parameters could be controlled, such as the balance shared/exclusive variances and the level of noise. We fitted the O2PLS and MANOPT models to the generated data: basically, O2PLS first identify the shared subspace between two areas, then subtracts the shared components to identify the exclusive subspace; in contrast, MANOPT iteratively optimized a functional on a Stifield matrix manifold considering both shared and exclusive contributions. As performance metrics, we calculated the R² of the reconstructed latent variables (I) and the differences between the variances explained by the subspaces with their real values (II). Results Both methods were able to retrieve the latent structure of the simulated data. However, the O2PLS algorithm offers fast fitting, but its performance depends on subspace balance. Indeed, when the shared subspace explained only 25% of correlated activity, the reconstruction accuracy (R²) for the shared variables was impacted (~0.70 vs. ~0.90 for exclusive ones). On the contrary, when the shared subspace dominated (75% variance) the shared variables could be reconstructed precisely (R²=0.94), while the exclusive were affected (0.64). In contrast, the optimization approach maintains robust performance (R² > 0.80) even in unbalanced subspace conditions, though at a higher computational cost (Fig. 1).Discussion During the data simulation, nonlinearities have not been explicitly considered since that the tested models are linear and precise mechanisms for nonlinearly mixing latent variables are unclear. However, we expected decreasing performance with increasing nonlinearities, maintaining the same overperformance of MANOPT observed in the linear case. We found that, given its fast computations, the O2PLS algorithm could be useful for exploratory analysis. However, for in depth data analysis, and in particular when the precise temporal evolution of latent dynamics is crucial, MANOPT approach should be preferred. Thus, MANOPT approach could represent the future standard method to dissecting shared and exclusive subspaces in neural activity analysis.
This work was supported by: project MNESYS (PE0000006) - A Multiscale integrated approach to the study of the nervous system in health and disease (DN. 1553 11.10.2022); Ministry of University and Research (MUR), PRIN2022-2022BK2NPS; grant H2020-EIC-FETPROACT-2019951910-MAIA
[1] Trygg, J., & Wold, S. (2003). O2
‐PLS, a two
‐block (X-Y) latent variable regression (LVR) method with an integral OSC filter.
Journal of chemometrics,
17(1), 53-64
[2] Jiang, X., Saggar, H., Ryu, S. I., Shenoy, K. V., & Kao, J. C. (2020). Structure in Neural Activity during Observed and Executed Movements Is Shared at the Neural Population Level, Not in Single Neurons.
Cell reports, 32(6), 108006 [3] Vaccari, F. E., Diomedi, S., Bettazzi, E., ..., & Fattori, P. (2024). More or fewer latent variables in the high-dimensional data space?
That is the question. bioRxiv, 2024-11
