(I-356) Non-Negative Matrix Factorization for Analysis of Latent Neuronal Network and Sub-Network Dynamics

Introduction:: Calcium imaging allows recording from hundreds of neurons in vivo with the ability to resolve single cell activity. Evaluating and analyzing neuronal responses, while also considering all dimensions of the data set to make specific conclusions, however, is extremely difficult. Often, descriptive statistics are used to analyze these forms of data. These analyses, however, remove variance by averaging the responses of single neurons across recording sessions or across combinations of neurons to create single quantitative metrics, losing the temporal dynamics of neuronal activity, and their responses relative to each other. Dimensionally Reduction (DR) methods, serve as a good foundation for these analyses because they reduce the dimensions of the data into components, while still maintaining the variance. Non-negative Matrix Factorization (NMF) is an especially promising DR analysis method for calcium imaging because of its mathematical constraints, which include positivity and linearity.

Materials and Methods:: We simulate an artificial “ground-truth” network to quantify the performance of NMF and its ability to extract pre-determined dynamics in the model network. We begin by generating five underlying random processes, and then generate 250 neurons, each of which receive an input from each random process. The input strength is randomly drawn from an exponential distribution (Fig 1a). We simulate 180 seconds of spiking for each neuron and convolve each neuron’s spike train with a calcium fluorescence kernel, whose parameters simulate our genetically encoded calcium indicator. The result is a statistically similar set of data to those extracted from recordings. We fit an NMF model to this network and quantify performance, where the resultant model is a matrix decomposition. The first matrix contains the weights of each neuron attributed to each reduced dimension, and the second matrix contains the activity of each reduced component.

Results, Conclusions, and Discussions:: Results & Discussion: We first evaluate the variance explained and the information criterion provided by the analysis of the model. Variance explained describes the portion of the variance each subsequently reduced dimension captures. Information criterion serves as a metric for model selection, which provides the number of components or subnetworks captured without overfitting. We find that variance explained begins to plateau, with the information criterion having a very clear inflection point at five components, the exact number of underlying processes driving the model network (Fig 1b). We then quantify how well each of the components recaptures one of the underlying processes by analyzing their pairwise correlations. We find the neuronal weights resulting from the analysis of the model are correlated at a rate of 0.94 to the inputs randomly drawn from the exponential distribution (Fig 1d, 1e). Further, when analyzing the correlations between the extracted activity components, and the initially generated underlying processes, they are correlated at a rate of 0.92 (Fig 1c).

Conclusions and Future Directions: We find that NMF can extract the inputs of the simulation (number of underlying processes, process activity, and generated neuron inputs) remarkably well, at a correlation of about 0.93 in a completely unsupervised fashion. NMF’s positivity and interpretability lead to exceptional performance in capturing the underlying dynamics of calcium activity, demonstrating its power as a tool in the analysis of network dynamics using calcium imaging methods.


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