Neural System Identification With Spike-Triggered Non-Negative Matrix Factorization

Abstract

Neuronal circuits formed in the brain are complex with intricate connection patterns. Such a 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 force 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.

Dissecting cascade computational components in spiking neural networks

“…The STNMF analysis was introduced in [ 17 ] and extended in [ 27 ]. Briefly, to reduce computational cost, we first applied pre-processing for the spike-triggered stimulus ensemble: for the i -th spike, the corresponding stimulus segment s ( τ ) i is weighted averaged by temporal STA filter k t : , such that time dimension τ is collapsed to a single frame of stimulus image for the i -th spike, termed effective stimulus image .…”

“…The STNMF weight matrix is specific to each individual spike of postsynaptic neurons. Thus, one can reconstruct all the possible spikes contributed by each presynaptic neuron [ 27 ]. In the two-layer model, LGN spikes were represented by incoming four RGCs, thus, each spike of LGN could be contributed by one of the RGCs.…”

“…Thus, STNMF decomposes the LGN response using each output spike and input stimulus image as illustrated in Fig 1B . As a consequence of matrix factorization, we obtained a single weight matrix and a number of modules, where the number of modules is exactly the number of presynaptic cells in the model. The benefit of STNMF is that the modules are corresponding to the spatial receptive fields of upstream presynaptic cells [17], and the weight matrix encodes the information of synaptic connections [27]. In addition, the STNMF can separate all spikes of a postsynaptic neuron into different subsets of spikes for each presynaptic neuron, as illustrated in Fig 1C . To illustrate the workflow of STNMF, we applied it to the model and analyzed the LGN spikes.…”

“…It has been used recently to identify functional units localized in space and time in neuronal activities [20][21][22][23][24][25][26]. STNMF takes a step further to analyze the mapping between stimuli and neural responses leveraging neural spikes while leaving out non-responsive stimuli [17,27], with an assist of spare coding, as neurons generally fire with a low rate of spikes [28].…”

Unraveling neural coding of dynamic natural visual scenes via convolutional recurrent neural networks

“…The recurrent layer plays an important role in modeling neuronal nonlinearity, which is a unique feature of neural computation. 60 By incorporating recurrent connections, many models have shown advantages in recognizing static images. 22,25,[61][62][63][64] An unrolled recurrent network is equivalent to a deeper or wider network that saves on neurons by repeating data transformation several times, 24,65,66 but it improves the flexibility trading of speed and accuracy in biological vision.…”