A detailed investigation of Shared Variance Component Analysis as a tool to characterize neural dimensionality

The relevance of spontaneous activity has been unlocked thanks to recent large scale recordings that revealed, via Shared Variance Component Analysis (SVCA), the high-dimensional nature of the ongoing activity. A fundamental problem is how the dimension is modified when more neurons are included in the analysis. Contradictory results have been reported on this subject based on SVCA and Principal Component Analysis (PCA).

We investigate pro et contra of SVCA and PCA for the identification of reliable responses encoding underlying state variables. We focus on common features of the spectra of the reliable variances (RVs) and on their dimensionality. The analysis is demonstrated on previously published Ca2⁺ data from the visual and the dorsal cortex in head fixed mice during spontaneous behavior.

RVs grow proportionally to the number N of neurons and show a power-law decay k^-α with the kth SVC dimension over a range bounded by a maximal dimension k_c, initially diverging as N^1/α and then saturating at sufficiently large N. The reliable dimensionality, estimated with different methodologies, also shows a clear saturation to an asymptotic value for large N. Furthermore, its value decreases when α becomes larger, as demonstrated by employing experimental data as well as theoretical predictions.

We have shown that SVCA is an extremely effective tool to extract reliable features from the neural signals, and that the exponent α represents a biomarker able to reveal the level of correlation of the neurons as well as the dimensionality of the reliable space.