Non-Negative Matrix Factorization for Analyzing State Dependent Neuronal Network Dynamics in Calcium Recordings.

Calcium imaging has enabled the unprecedented recording of complex brain activity in novel contexts. Recording activity from hundreds of single neurons within a specific brain region, it allows study of local networks that was previously inaccessible. However, these recordings create increasingly large data sets. Manually analyzing every neuron's activity, and meaningfully relating it to every other neuron's is impossible in practice. Nearly all analyses use descriptive statistics to simply summarize the activity found in these recordings, simplifying at the expense of discounting the nuance found in such complicated data. Dimensionality Reduction (DR) provides a machine learning alternative to comprehensively analyze the data, significantly reducing complexity, while considering both each neuron's activity, and the relationships between them. Non-Negative Matrix Factorization (NMF) is especially promising for analysis of these recordings because of its mathematical constraints of linearity and positivity. We compare several DR methods to NMF below, using simulated neuronal networks with statistically similar activity to our recordings, before applying it to a series of awake baseline recordings as a proof of concept on recorded data. We demonstrate NMF significantly outperforms every other method tested, proving it a promisingly powerful tool for analyzing network dynamics to study unique neural contexts.