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  Connectome smoothing via low-rank approximations

Tang, R., Ketcha, M., Badea, A., Calabrese, E. D., Margulies, D. S., Vogelstein, J. T., et al. (2018). Connectome smoothing via low-rank approximations. arXiv.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0002-B429-5 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-FB30-D
Genre: Paper

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 Creators:
Tang, Runze 1, Author
Ketcha, Michael 2, Author
Badea, Alexandra 3, Author
Calabrese, Evan D.3, Author
Margulies, Daniel S.4, 5, Author              
Vogelstein, Joshua T. 2, 6, Author
Priebe, Carey E. 1, Author
Sussman, Daniel L. S5, Author
Affiliations:
1Department of Applied Math and Statistics, Johns Hopkins University, Baltimore, MD, ou_persistent22              
2Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, ou_persistent22              
3Department of Radiology, and Department of Biomedical Engineering, Duke University, Durham, NC, ou_persistent22              
4Max Planck Research Group Neuroanatomy and Connectivity, MPI for Human Cognitive and Brain Sciences, Max Planck Society, ou_1356546              
5Child Mind Institute, New York, NY, ou_persistent22              
6Department of Mathematics and Statistics, Boston University, Boston, MA, ou_persistent22              

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Free keywords: networks; connectome; low-rank; estimation
 Abstract: In statistical connectomics, the quantitative study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject. While using the element-wise sample mean of the adjacency matrices is a common approach, this method does not exploit any underlying structural properties of the graphs. We propose using a low-rank method which incorporates tools for dimension selection and diagonal augmentation to smooth the estimates and improve performance over the naive methodology for small sample sizes. Theoretical results for the stochastic blockmodel show that this method offers major improvements when there are many vertices. Similarly, we demonstrate that the low-rank methods outperform the standard sample mean for a variety of independent edge distributions as well as human connectome data derived from magnetic resonance imaging, especially when sample sizes are small. Moreover, the low-rank methods yield "eigen-connectomes", which correlate with the lobe-structure of the human brain and superstructures of the mouse brain. These results indicate that low-rank methods are an important part of the tool box for researchers studying populations of graphs in general, and statistical connectomics in particular.

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Language(s): eng - English
 Dates: 2018-12-062016-09-062018-12-06
 Publication Status: Published online
 Pages: -
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 Rev. Type: No review
 Identifiers: arXiv: 1609.01672
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Title: arXiv
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