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Statistical Analysis of Trajectories of Multi-Modality Data

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Handbook of Variational Methods for Nonlinear Geometric Data

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Abstract

We develop a novel comprehensive Riemannian framework for analyzing, summarizing and clustering trajectories of multi-modality data. Our framework relies on using elastic representations of functions, curves and trajectories. The elastic representations not only provide proper distances, but also solve the problem of registration. We propose a proper Riemannian metric, which is a weighted average of distances on product spaces. The metric allows for joint comparison and registration of multi-modality data. Specifically, we apply our framework to detect stimulus-relevant fiber pathways and summarize projection pathways. We evaluate our method on two real data sets. Experimental results show that we can cluster fiber pathways correctly and compute better summaries of projection pathways. The proposed framework can also be easily generalized to various applications where multi-modality data exist.

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Author information

Authors and Affiliations

  1. Harbin Institute of Technology (Shenzhen), Shenzhen, China

    Jingyong Su

  2. Texas Tech University, Lubbock, TX, USA

    Mengmeng Guo

  3. Sichuan University, Chengdu, China

    Zhipeng Yang

  4. Vanderbilt University, Nashville, TN, USA

    Zhaohua Ding

Authors
  1. Jingyong Su
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  2. Mengmeng Guo
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  3. Zhipeng Yang
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  4. Zhaohua Ding
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Correspondence to Jingyong Su .

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Editors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Wien, Austria

    Philipp Grohs

  2. Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria

    Martin Holler

  3. Department of Mathematics and Natural Sciences, Hochschule Darmstadt, Darmstadt, Germany

    Andreas Weinmann

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Su, J., Guo, M., Yang, Z., Ding, Z. (2020). Statistical Analysis of Trajectories of Multi-Modality Data. In: Grohs, P., Holler, M., Weinmann, A. (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, Cham. https://doi.org/10.1007/978-3-030-31351-7_14

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