hdnet stands for Hopfield denoising network. It is a Python package for analysis of neural population spiking data, i.e. parallel spike trains.

In particular, it provides a novel method for finding and extracting salient low-dimensional representations of the dynamics of populations of spiking neurons based on a denoising approach to spatiotemporal patterns (STP) contained in the data.

Finding STP is classical problem in data analysis of parallel spike trains, and quite a number of approaches to detect and classify recurring spatiotemporal patterns (STP) of neural population activity were proposed [1].

Yet, most published methods so far either focus solely on synchrony detection [2, 3, 4] or assume a more or less noiseless scenario, seeking to classify exactly recurring STP in neuronal activity (apart from allowing some jitter in spike timing), see e.g. [5]. Some furthermore suffer from effects of combinatorial explosion [3, 5], making their application to highly parallel neural recordings a hard computational problem.

Given the usually high variability of population responses to stimuli, the re-occurrence of such exactly repeating STP becomes more and more unlikely with increasing population size, though. Assuming that despite this variability, network activity is not random per se (under the experimentally well-supported hypothesis [6, 7] that the population has to code information about stimuli in some form of STP), a much more plausible situation is that some underlying STP appears in several "corrupted" variants, both expressing jitter in spike times and differing in a few missing or excess spikes (characterized by a low Hamming distance to a true, underlying STP).

Our method takes a different aproach. Using Hopfield networks trained with minimum energy flow (MEF), the occuring raw spatiotemporal patterns are grouped into clusters of similar patterns in an unsupervised way, assigning to each cluster a memory (the fixed point of the Hopfield dynamics in each cluster).

The proposed method is robust to this variability in the signal and able to extract the underlying recurring patterns, even for seldomly occurring STP and large population sizes.

The package ships with a tutorial and is extensively documented.

Papers Using HDNET:

[A] Hillar, Christopher and Sohl-Dickstein, Jascha and Koepsell, Kilian, Efficient and optimal binary Hopfield associative memory storage using minimum probability flow, 2012. https://arxiv.org/abs/1204.2916v1

[B] Hillar, Christopher and Mehta, Ram and Koepsell, Kilian, A Hopfield recurrent neural network trained on natural images performs state-of-the-art image compression, 2014 IEEE International Conference on Image Processing (ICIP), 2014. https://ieeexplore.ieee.org/document/7025831

[C] Hillar, Christopher, and Felix Effenberger. "Robust discovery of temporal structure in multi-neuron recordings using hopfield networks." Procedia Computer Science 53 (2015): 365-374. https://www.sciencedirect.com/science/article/pii/S1877050915018165

[D] Effenberger, Felix, and Christopher Hillar. "Discovery of salient low-dimensional dynamical structure in neuronal population activity using hopfield networks." In International Workshop on Similarity-Based Pattern Recognition, pp. 199-208. Springer, Cham, 2015. https://link.springer.com/chapter/10.1007/978-3-319-24261-3_16

[E] Mehta, Ram and Marzen, Sarah and Hillar, Christopher, Exploring discrete approaches to lossy compression schemes for natural image patches, 2015 23rd European Signal Processing Conference (EUSIPCO), 2015. https://ieeexplore.ieee.org/document/7362782

[F] Hillar, Christopher and Marzen, Sarah, Revisiting perceptual distortion for natural images: Mean discrete structural similarity index, 2017 Data Compression Conference (DCC), 2017. https://ieeexplore.ieee.org/abstract/document/7921919

[G] Hillar, Christopher J and Marzen, Sarah E, Neural network coding of natural images with applications to pure mathematics, Contemporary Mathematics; American Mathematical Sociecty: Providence, RI, USA, 2017. https://www.researchgate.net/publication/315352597_Neural_network_coding_of_natural_images_with_applications_to_pure_mathematics

[H] Hillar, Christopher J and Tran, Ngoc M, Robust exponential memory in Hopfield networks, The Journal of Mathematical Neuroscience, 2018. https://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-017-0056-2

[I] Hillar, Chan, Taubman, Rolnick, Hidden Hypergraphs, Error-Correcting Codes, and Critical Learning in Hopfield Networks, Entropy, 2021. https://www.mdpi.com/1099-4300/23/11/1494/htm

[J] Lamberti, Martina and Hess, Michael and Dias, In{^e}s and van Putten, Michel and le Feber, Joost and Marzen, Sarah, Maximum entropy models provide functional connectivity estimates in neural networks, Scientific Reports, 2022. https://www.nature.com/articles/s41598-022-13674-4

Others:

[1] S. Grün and S. Rotter. Analysis of parallel spike trains. Springer, 2010
[2] G. Pipa, D. W. Wheeler, W. Singer, and D. Nikolić. NeuroXidence: reliable and efficient analysis of an excess or deficiency of joint-spike events. Journal of Computational Neuroscience, 25(1):64–88, 2008.
[3] D. Picado-Muiño, C. Borgelt, D. Berger, G. Gerstein, and S. Grün. Finding neural assemblies with frequent item set mining. Frontiers in neuroinformatics, 7(May):9, 2013.
[4] V. Lopes-dos-Santos, S. Ribeiro, and A. B. L. Tort. Detecting cell assemblies in large neuronal populations. Journal of Neuroscience Methods, 220(2):149–66, 2013.
[5] K. S. Gansel and W. Singer. Detecting multineuronal temporal patterns in parallel spike trains. Frontiers in Neuroinformatics, 6(May):18, 2012.
[6] M. Abeles and H. Bergman. Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. Journal of Neurophysiology, 1993.
[7] A. Arieli and D. Shoham. Coherent spatiotemporal patterns of ongoing activity revealed by real-time optical imaging coupled with single-unit recording in the cat visual cortex. Journal of Neurophysiology, 1995.

Until we provide an official release, please install hdnet directly from Github using pip.

To install / update to the latest version use:

pip install git+ssh://git@github.com/team-hdnet/hdnet.git

To install a specific version, use:

pip install git+ssh://git@github.com/team-hdnet/hdnet@VERSION,

where VERSION is v0.1 for example. See releases tab above for released versions.

View the documentation (online and PDF version available).

If you use hdnet in your work please cite it using the following BibTeX entry.

@online{hdnet,
    author      = {Hillar, Christopher  and Effenberger, Felix},
    title       = {\texttt{hdnet} -- a Python package for parallel spike train analysis},
    year        = {2015},
    url         = {https://github.com/team-hdnet/hdnet}
}

Christopher Hillar
Redwood Center for Theoretical Neuroscience
UC Berkeley, Berkeley, CA, USA
E-mail: hillarmath@gmail.com

Felix Effenberger
Max-Planck-Institute for Mathematics in the Sciences
Leipzig, Germany
E-mail: Felix.Effenberger@mis.mpg.de

For non-commercial use, hdnet is licensed under the GNU GPLv3, see file LICENSE. For use in commercial projects please contact the authors for licensing options.

We are looking for contributors! If you are interested in contributing or find a bug, please contact us personally or via a pull request!

• Install required modules pip install sphinx sphinx_rtd_theme sphinxcontrib-napoleon sphinxcontrib-bibtex sphinxjp.themes.basicstrap

• Build documentation: HTML: make html LaTeX: make latexpdf

• Built documentation can be found in doc/_build/html and doc/_build/latex