Abstract
We present a combinatorial algorithm for cell detection in two-photon calcium imaging. Calcium imaging is a modern technique used by neuroscientists for recording movies of in-vivo neuronal activity at cellular resolution. The proposed algorithm, named HNCcorr, builds on the combinatorial clustering problem Hochbaum’s Normalized Cut (HNC). HNC is a model that trades off two goals: One goal is that the cluster has low similarity to the remaining objects. The second goal is that the cluster is highly similar to itself. The HNC model is closely related to the Normalized Cut problem of Shi and Malik, a well-known problem in image segmentation. However, whereas Normalized Cut is an NP-hard problem, HNC is solvable in polynomial time. The neuronal cell detection in calcium imaging movies is viewed here as a clustering problem. HNCcorr utilizes HNC to detect cells in these movies as coherent clusters of pixels that are highly distinct from the remaining pixels. HNCcorr guarantees, unlike existing methodologies for cell identification, a globally optimal solution to the underlying optimization problem. Of independent interest is a novel method, named similarity-squared, that is devised here for measuring similarity. In an experimental study on data from the Neurofinder cell identification benchmark, HNCcorr is a top performer. In particular, it achieves a higher average score than two frequently used matrix factorization algorithms. The Python and Matlab implementations of HNCcorr used here are publicly available. The use of HNCcorr demonstrates that combinatorial optimization is a valuable tool for neuroscience and other biomedical disciplines.
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Notes
See e.g. issues 16 and 24 on https://github.com/codeneuro/neurofinder.
References
Apthorpe, N., Riordan, A., Aguilar, R., Homann, J., Gu, Y., Tank, D., & Seung, H.S. (2016). Automatic neuron detection in calcium imaging data using convolutional networks. In Advances in neural information processing systems (pp. 3270–3278)
Baumann, P., Hochbaum, D.S., & Spaen, Q. (2016). Sparse-reduced computation: Enabling mining of massively-large data sets. In Proceedings of the 5th international conference on pattern recognition applications and methods, SCITEPRESS, Rome, Italy (pp. 224–231)
Baumann, P., Hochbaum, D.S., & Spaen, Q. (2017). High-performance geometric algorithms for sparse computation in big data analytics. In 2017 IEEE International Conference on Big Data (Big Data) (pp. 546–555)
Baumann, P., Hochbaum, D., & Yang, Y. (2019). A comparative study of the leading machine learning techniques and two new optimization algorithms. European Journal of Operational Research, 272(3), 1041–1057.
Berens, P., Freeman, J., Deneux, T., Chenkov, N., McColgan, T., Speiser, A., et al. (2018). Community-based benchmarking improves spike rate inference from two-photon calcium imaging data. PLoS Computational Biology, 14(5), e1006157.
CodeNeuro (2016). The neurofinder challenge. http://neurofinder.codeneuro.org/. Accessed June 01, 2018
Cortes, C., & Vapnik, V. (1995). Support-vector networks. Machine Learning, 20(3), 273–297.
Dembczyński, K., Kotłowski, W., & Słowiński, R. (2009). Learning rule ensembles for ordinal classification with monotonicity constraints. Fundamenta Informaticae, 94(2), 163–178.
Diego-Andilla, F., & Hamprecht, F.A. (2014). Sparse space-time deconvolution for calcium image analysis. In Advances in neural information processing systems (pp. 64–72)
Drineas, P., Kannan, R., & Mahoney, M. W. (2006). Fast monte carlo algorithms for matrices ii: Computing a low-rank approximation to a matrix. SIAM Journal on Computing, 36(1), 158–183.
Driscoll, L. N., Pettit, N. L., Minderer, M., Chettih, S. N., & Harvey, C. D. (2017). Dynamic reorganization of neuronal activity patterns in parietal cortex. Cell, 170(5), 986–999.
Fishbain, B., Hochbaum, D.S., & Yang, Y.T. (2013). Real-time robust target tracking in videos via graph-cuts. In Real-time image and video processing 2013, international society for optics and photonics, (Vol. 8656, p. 865602)
Frey, P. W., & Slate, D. J. (1991). Letter recognition using Holland-style adaptive classifiers. Machine Learning, 6(2), 161–182.
Gallo, G., Grigoriadis, M. D., & Tarjan, R. E. (1989). A fast parametric maximum flow algorithm and applications. SIAM Journal on Computing, 18(1), 30–55.
Gao, S. (2016). Conv2d: Convolutional neural network. https://github.com/iamshang1/Projects/tree/master/Advanced_ML/Neuron_Detection. Accessed June 01, 2018
Giovannucci, A., Friedrich, J., Kaufman, M., Churchland, A., Chklovskii, D., Paninski, L., & Pnevmatikakis, E.A. (2017) Onacid: Online analysis of calcium imaging data in real time. In Advances in neural information processing systems (pp. 2381–2391)
Goldberg, A. V., & Tarjan, R. E. (1988). A new approach to the maximum-flow problem. J ACM, 35(4), 921–940.
Grewe, B. F., Langer, D., Kasper, H., Kampa, B. M., & Helmchen, F. (2010). High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision. Nature Methods, 7(5), 399–405.
Hochbaum, D. S. (2002). Solving integer programs over monotone inequalities in three variables: A framework for half integrality and good approximations. European Journal of Operational Research, 140(2), 291–321.
Hochbaum, D. S. (2008). The pseudoflow algorithm: A new algorithm for the maximum-flow problem. Operations Research, 56(4), 992–1009.
Hochbaum, D. S. (2010). Polynomial Time Algorithms for Ratio Regions and a Variant of Normalized Cut. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(5), 889–898.
Hochbaum, D. S. (2013). A polynomial time algorithm for rayleigh ratio on discrete variables: Replacing spectral techniques for expander ratio, normalized cut, and cheeger constant. Operations Research, 61(1), 184–198.
Hochbaum, D. S., & Baumann, P. (2016). Sparse computation for large-scale data mining. IEEE Transactions on Big Data, 2(2), 151–174.
Hochbaum, D. S., & Fishbain, B. (2011). Nuclear threat detection with mobile distributed sensor networks. Annals of Operations Research, 187(1), 45–63.
Hochbaum, D. S., Hsu, C. N., & Yang, Y. T. (2012). Ranking of multidimensional drug profiling data by fractional-adjusted bi-partitional scores. Bioinformatics, 28(12), i106–i114.
Hochbaum, D. S., Lyu, C., & Bertelli, E. (2013). Evaluating performance of image segmentation criteria and techniques. EURO Journal on Computational Optimization, 1(1), 155–180.
Jewell, S., & Witten, D. (2018). Exact spike train inference via \$\(\backslash \)ell\_{0}\$ optimization. The Annals of Applied Statistics, 12(4), 2457–2482.
Jia, H., Rochefort, N. L., Chen, X., & Konnerth, A. (2011). In vivo two-photon imaging of sensory-evoked dendritic calcium signals in cortical neurons. Nature Protocols, 6(1), 28.
Kaifosh, P., Zaremba, J. D., Danielson, N. B., & Losonczy, A. (2014). SIMA: Python software for analysis of dynamic fluorescence imaging data. Frontiers in Neuroinformatics, 8, 40.
Klibisz, A., Rose, D., Eicholtz, M., Blundon, J., & Zakharenko, S. (2017). Fast, simple calcium imaging segmentation with fully convolutional networks. In M. J. Cardoso, T. Arbel, G. Carneiro, T. Syeda-Mahmood, J. M. R. Tavares, M. Moradi, A. Bradley, H. Greenspan, J. P. Papa, A. Madabhushi, J. C. Nascimento, J. S. Cardoso, V. Belagiannis, & Z. Lu (Eds.), Deep learning in medical image analysis and multimodal learning for clinical decision support. lecture notes in computer science (pp. 285–293). Berlin: Springer.
Levin-Schwartz, Y., Sparta, D. R., Cheer, J. F., & Adalı, T. (2017). Parameter-free automated extraction of neuronal signals from calcium imaging data. IEEE international conference on acoustics. Speech and signal processing (pp. 1033–1037). IEEE
Maruyama, R., Maeda, K., Moroda, H., Kato, I., Inoue, M., Miyakawa, H., et al. (2014). Detecting cells using non-negative matrix factorization on calcium imaging data. Neural Networks, 55, 11–19.
Mukamel, E. A., Nimmerjahn, A., & Schnitzer, M. J. (2009). Automated analysis of cellular signals from large-scale calcium imaging data. Neuron, 63(6), 747–760.
Pachitariu, M., Packer, A.M., Pettit, N., Dalgleish, H., Hausser, M., & Sahani, M. (2013). Extracting regions of interest from biological images with convolutional sparse block coding. In Advances in neural information processing systems (pp 1745–1753)
Pachitariu, M., Stringer, C., Dipoppa, M., Schröder, S., Rossi, L.F., Dalgleish, H., Carandini, M., & Harris, K.D. (2017). Suite2p: beyond 10,000 neurons with standard two-photon microscopy. bioRxiv p 061507
Pnevmatikaki, E.A., & Paninski, L. (2013). Sparse nonnegative deconvolution for compressive calcium imaging: Algorithms and phase transitions. In Advances in neural information processing systems (pp. 1250–1258)
Pnevmatikakis, E.A., Merel, J., Pakman, A., & Paninski, L. (2013). Bayesian spike inference from calcium imaging data. In Asilomar conference on signals, systems and computers (pp. 349–353)
Pnevmatikakis, E. A., Soudry, D., Gao, Y., Machado, T. A., Merel, J., Pfau, D., et al. (2016). Simultaneous denoising, deconvolution, and demixing of calcium imaging data. Neuron, 89(2), 285–299.
Resendez, S. L., Jennings, J. H., Ung, R. L., Namboodiri, V. M. K., Zhou, Z. C., Otis, J. M., et al. (2016). Visualization of cortical, subcortical, and deep brain neural circuit dynamics during naturalistic mammalian behavior with head-mounted microscopes and chronically implanted lenses. Nature Protocols, 11(3), 566.
Ryu, Y. U., Chandrasekaran, R., & Jacob, V. (2004). Prognosis using an isotonic prediction technique. Management Science, 50(6), 777–785.
Sharon, E., Galun, M., Sharon, D., Basri, R., & Brandt, A. (2006). Hierarchy and adaptivity in segmenting visual scenes. Nature, 442(7104), 810–813.
Shi, J., & Malik, J. (2000). Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8), 888–905.
Stosiek, C., Garaschuk, O., Holthoff, K., & Konnerth, A. (2003). In vivo two-photon calcium imaging of neuronal networks. Proceedings of the National Academy of Sciences, 100(12), 7319–7324.
Theis, L., Berens, P., Froudarakis, E., Reimer, J., Rosón, M. R., Baden, T., et al. (2016). Benchmarking spike rate inference in population calcium imaging. Neuron, 90(3), 471–482.
Vogelstein, J. T., Packer, A. M., Machado, T. A., Sippy, T., Babadi, B., Yuste, R., et al. (2010). Fast nonnegative deconvolution for spike train inference from population calcium imaging. Journal of Neurophysiology, 104(6), 3691–3704.
Yang, Y. T., Fishbain, B., Hochbaum, D. S., Norman, E. B., & Swanberg, E. (2013). The supervised normalized cut method for detecting, classifying, and identifying special nuclear materials. INFORMS Journal on Computing, 26(1), 45–58.
Zhu, X. R., Yoo, S., Jursinic, P. A., Grimm, D. F., Lopez, F., Rownd, J. J., et al. (2003). Characteristics of sensitometric curves of radiographic films. Medical Physics, 30(5), 912–919.
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The fund was supported by Division of Civil, Mechanical and Manufacturing Innovation (Grant No. 1760102).
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Asín Achá, R., Hochbaum, D.S. & Spaen, Q. HNCcorr: combinatorial optimization for neuron identification. Ann Oper Res 289, 5–32 (2020). https://doi.org/10.1007/s10479-019-03464-z
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DOI: https://doi.org/10.1007/s10479-019-03464-z