[Paper Review] Neural System Identification with Spike-triggered Non-negative Matrix Factorization

Shanshan Jia, Zhaofei Yu+4 more|arXiv (Cornell University)|Aug 12, 2018

Neural dynamics and brain function68 references4 citations

TL;DR

This paper proposes Spike-Triggered Non-negative Matrix Factorization (STNMF) as a method to identify functional and structural properties of retinal neural circuits by analyzing ganglion cell spiking responses. It reveals that STNMF can extract spatial receptive fields, temporal filters, nonlinearities, synaptic weights, and classify spikes according to their presynaptic bipolar cell origin, demonstrating its power for unsupervised system identification in neuroscience.

ABSTRACT

Neuronal circuits formed in the brain are complex with intricate connection patterns. Such complexity is also observed in the retina as a relatively simple neuronal circuit. A retinal ganglion cell receives excitatory inputs from neurons in previous layers as driving forces to fire spikes. Analytical methods are required that can decipher these components in a systematic manner. Recently a method termed spike-triggered non-negative matrix factorization (STNMF) has been proposed for this purpose. In this study, we extend the scope of the STNMF method. By using the retinal ganglion cell as a model system, we show that STNMF can detect various computational properties of upstream bipolar cells, including spatial receptive field, temporal filter, and transfer nonlinearity. In addition, we recover synaptic connection strengths from the weight matrix of STNMF. Furthermore, we show that STNMF can separate spikes of a ganglion cell into a few subsets of spikes where each subset is contributed by one presynaptic bipolar cell. Taken together, these results corroborate that STNMF is a useful method for deciphering the structure of neuronal circuits.

Motivation & Objective

• To develop a systematic, data-driven method for identifying functional components of retinal neural circuits from spike train recordings.
• To extend the STNMF framework beyond subunit localization to extract detailed computational properties such as spatial receptive fields, temporal filters, and transfer nonlinearities.
• To recover synaptic connection strengths between bipolar cells and retinal ganglion cells using the STNMF weight matrix.
• To classify ganglion cell spikes into distinct subsets, each associated with a specific presynaptic bipolar cell, enabling functional deconvolution of input sources.

Proposed method

• Apply spike-triggered non-negative matrix factorization (STNMF) to retinal ganglion cell spiking responses triggered by white-noise checkerboard stimuli.
• Use a minimal two-layer neural network model with spatial filters, temporal filters (e.g., OFF filters), and threshold-linear nonlinearities to simulate retinal circuit dynamics.
• Factorize the spike-triggered average (STA) or spike-triggered covariance (STC) data using NMF with non-negativity constraints to extract meaningful components.
• Decode the STNMF weight matrix to assign each spike to a specific presynaptic bipolar cell, enabling spike subset classification.
• Validate results using both synthetic data with known ground truth and real retinal ganglion cell recordings.
• Integrate sparseness constraints to enhance the interpretability of learned components, aligning with the local receptive field structure of sensory neurons.

Experimental results

Research questions

• RQ1 Can STNMF extract spatial receptive fields and temporal filters of upstream bipolar cells from ganglion cell spike responses?
• RQ2 Can STNMF recover the transfer nonlinearity (e.g., threshold-linear) of bipolar cell to ganglion cell synapses?
• RQ3 Can STNMF estimate synaptic weights between individual bipolar cells and the ganglion cell?
• RQ4 Can STNMF classify ganglion cell spikes into distinct subsets, each corresponding to a different presynaptic bipolar cell?
• RQ5 How well does STNMF perform in identifying circuit components when applied to real biological retinal data with unknown ground truth?

Key findings

• STNMF successfully recovers the spatial receptive fields of bipolar cells, accurately localizing subunit inputs to 2×2 pixel regions in the stimulus.
• The method identifies temporal filters, including OFF-type dynamics, consistent with known retinal circuit physiology.
• STNMF recovers the transfer nonlinearity of bipolar cells, showing threshold-linear behavior that matches the simulated model.
• Synaptic weights derived from the STNMF weight matrix correlate with known connection strengths in the simulated network.
• STNMF classifies ganglion cell spikes into distinct subsets, each strongly associated with a single presynaptic bipolar cell, as confirmed by ground-truth data.
• When applied to real retinal ganglion cell data, STNMF produces similar results, indicating robustness and biological relevance of the method.