Simulation of fronto-parietal neural population activity to probe dimensionality reduction methods.

by Andrej Filippow
Doctoral thesis
Date of Examination:2021-09-28
Date of issue:2022-09-20
Advisor:Prof. Dr. Hansjörg Scherberger
Referee:Prof. Dr. Alexander Gail
Referee:Prof. Dr. Florentin Wörgötter
Persistent Address: http://dx.doi.org/10.53846/goediss-9450

 

 

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Abstract

English

Recent developments of optical and electrophysiological recording tools allow the detailed capture of large neuronal populations. Findings show that their activity is constrained to a low-dimensional manifold within the full space of neuronal firing rates, a manifold spanned by a comparatively small number of task-related Latent Variables (LVs). One key goal of population analysis is to extract this low-dimensional manifold / response structure and identify the latent variables.To this end, many recent studies use approaches based on Principal Component Analysis (PCA). Even though PCA has been analyzed in general, and several conceptual weaknesses have been noted before, the applicability of PCA to neuronal data has not been studied in detail. In this paper we use a biologically plausible simulation of the spiking neuronal response to two manual tasks to evaluate the performance of PCA in extracting the low-dimensional manifold / structure and recovering the underlying latent variables. We find that the limiting parameter for PCA is the number of trials recorded per condition. For sufficiently high numbers PCA can successfully extract the manifold / structure. On the other hand, it is difficult to estimate the correct number of LVs from the results of PCA. Furthermore, principal components are arbitrary linear combinations of the true LVs and it’s impossible to recover the LVs in an unmixed fashion from the results of PCA.
Keywords: Dimensionality Reduction, Neural population response, PCA
 
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