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Quantitative Arbor Analytics: Unsupervised Harmonic Co-Clustering of Populations of Brain Cell Arbors Based on L-Measure

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Abstract

This paper presents a robust unsupervised harmonic co-clustering method for profiling arbor morphologies for ensembles of reconstructed brain cells (e.g., neurons, microglia) based on quantitative measurements of the cellular arbors. Specifically, this method can identify groups and sub-groups of cells with similar arbor morphologies, and simultaneously identify the hierarchical grouping patterns among the quantitative arbor measurements. The robustness of the proposed algorithm derives from use of the diffusion distance measure for comparing multivariate data points, harmonic analysis theory, and a Haar-like wavelet basis for multivariate data smoothing. This algorithm is designed to be practically usable, and is embedded into the actively linked three-dimensional (3-D) visualization and analytics system in the free and open source FARSIGHT image analysis toolkit for interactive exploratory population-scale neuroanatomic studies. Studies on synthetic datasets demonstrate its superiority in clustering data matrices compared to recent hierarchical clustering algorithms. Studies on heterogeneous ensembles of real neuronal 3-D reconstructions drawn from the NeuroMorpho database show that the proposed method identifies meaningful grouping patterns among neurons based on arbor morphology, and revealing the underlying morphological differences.

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Information Sharing Statement

A FARSIGHT (RRID:nif-0000-10227) Wiki website provides detailed information about the open-source software system reported in this paper. The software system will be distributed as source code and installable executable for common operating systems. The website is available at: http://www.farsight-toolkit.org/wiki/Main_Page. The neuronal reconstruction datasets used in the experiments are available at: http://neuromorpho.org/neuroMorpho/index.jsp (RRID:nif-0000-00006).

Acknowledgements

This work was supported by DARPA Grant N66001-11-1-4015. We thank Audrey Cheong and Jonathan Luisi for collaborative assistance, and Sridevi Polavaram in Dr. Giorgio Ascoli’s laboratory for assistance with the L-Measure software library.

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Authors and Affiliations

  1. Department of Electrical & Computer Engineering, University of Houston, Houston, TX, USA

    Yanbin Lu & Badrinath Roysam

  2. Department of Electrical & Computer Engineering, Duke University, Durham, NC, USA

    Lawrence Carin

  3. Department of Mathematics, Yale University, New Haven, CT, USA

    Ronald Coifman

  4. Center for Integrative Brain Research, Seattle Children’s Research Institute, Seattle, WA, USA

    William Shain

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  1. Yanbin Lu
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Correspondence to Badrinath Roysam.

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Lu, Y., Carin, L., Coifman, R. et al. Quantitative Arbor Analytics: Unsupervised Harmonic Co-Clustering of Populations of Brain Cell Arbors Based on L-Measure. Neuroinform 13, 47–63 (2015). https://doi.org/10.1007/s12021-014-9237-2

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