Discovery of Salient Low-Dimensional Dynamical Structure in Neuronal Population Activity Using Hopfield Networks
We present here a novel method for the classical task of finding and extracting recurring spatiotemporal patterns in recorded spiking activity of neuronal populations. In contrast to previously proposed methods it does not seek to classify exactly recurring patterns, but rather approximate versions possibly differing by a certain number of missed, shifted or excess spikes. We achieve this by fitting large Hopfield networks to windowed, binned spiking activity in an unsupervised way using minimum probability flow parameter estimation and then collect Hopfield memories over the raw data. This procedure results in a drastic reduction of pattern counts and can be exploited to identify prominently recurring spatiotemporal patterns. Modeling furthermore the sequence of occurring Hopfield memories over the original data as a Markov process, we are able to extract low-dimensional representations of neural population activity on longer time scales. We demonstrate the approach on a data set obtained in rat barrel cortex and show that it is able to extract a remarkably low-dimensional, yet accurate representation of population activity observed during the experiment.
KeywordsNeuronal population activity Parallel spike train analysis Spatiotemporal patterns Hopfield network Ising model
The authors would like to thank Yuri Campbell for helpful comments on an earlier version of this manuscript.
- 1.Abeles, M., Bergman, H.: Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J. Neurophysiol. 70(4), 1629–1638 (1993)Google Scholar
- 2.Arieli, A., Shoham, D.: Coherent spatiotemporal patterns of ongoing activity revealed by real-time optical imaging coupled with single-unit recording in the cat visual cortex. J. Neurophysiol. 73(5), 2072–2093 (1995)Google Scholar
- 5.Gansel, K.S., Singer, W.: Detecting multineuronal temporal patterns in parallel spike trains. Front. Neuroinformatics 6(May), 18 (2012)Google Scholar
- 7.Hillar, C., Effenberger, F.: hdnet - hopfield denoising network. https://github.com/team-hdnet/hdnet (2015)
- 8.Hillar, C., Sohl-Dickstein, J., Koepsell, K.: Efficient and optimal little-hopfield auto-associative memory storage using minimum probability flow. In: NIPS Workshop on Discrete Optimization in Machine Learning (DISCML) (2012)Google Scholar
- 10.Hillar, C., Tran, N.: Robust exponential memory in Hopfield networks. arXiv e-prints (2014)Google Scholar
- 15.Picado-Muiño, D., Borgelt, C., Berger, D., Gerstein, G., Grün, S.: Finding neural assemblies with frequent item set mining. Front. Neuroinformatics 7(May), 9 (2013)Google Scholar