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Multiscale network analysis through tail-greedy bottom-up approximation, with applications in neuroscience

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Listed:
  • Kang, Xinyu
  • Fryzlewicz, Piotr
  • Chu, Catherine
  • Kramer, Mark
  • Kolaczyk, Eric D.

Abstract

We propose the TGUH (Tail-Greedy Unbalanced Haar) transform for networks, which results in an orthonormal, adaptive decomposition of the network adjacency matrix into Haar-wavelet like components. The `tail-greediness' of the algorithm - indicating multiple greedy steps are taken in a single pass through the data - enables both fast computation and consistent estimation of network signals. We focus on development of our multiscale network decomposition and a corresponding method for network signal denoising. Moreover, we establish consistency of our resulting denoising methodology, present numerical simulations illustrating compression, and illustrate through application to signals on diffusion tensor imaging (DTI) networks.

Suggested Citation

  • Kang, Xinyu & Fryzlewicz, Piotr & Chu, Catherine & Kramer, Mark & Kolaczyk, Eric D., 2018. "Multiscale network analysis through tail-greedy bottom-up approximation, with applications in neuroscience," LSE Research Online Documents on Economics 90021, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:90021
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    References listed on IDEAS

    as
    1. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    2. Fryzlewicz, Piotr & Timmermans, Catherine, 2016. "SHAH: SHape-Adaptive Haar wavelets for image processing," LIDAM Reprints ISBA 2016043, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Fionn Murtagh, 2007. "The Haar Wavelet Transform of a Dendrogram," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 3-32, June.
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    More about this item

    Keywords

    Matrix decomposition; Wavelet transforms; Noise reduction; Sparse matrices; Electronic mail; Estimation; EP/L014246/1; 1R01NS095369-01;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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