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PATENet: Pairwise Alignment of Time Evolving Networks

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Machine Learning and Data Mining in Pattern Recognition (MLDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10934))

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Abstract

Networks that change over time, e.g. functional brain networks that change their structure due to processes such as development or aging, are naturally modeled by time-evolving networks. In this paper we present PATENet, a novel method for aligning time-evolving networks. PATENet offers a mathematically-sound approach to aligning time evolving networks. PATENet leverages existing similarity measures for networks with fixed topologies to define well-behaved similarity measures for time evolving networks. We empirically explore the behavior of PATENet through synthetic time evolving networks under a variety of conditions.

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Notes

  1. 1.

    Notice that \( \tilde{\chi }:{\mathcal{G}} \times {\mathcal{G}}^{'} \to {\mathbb{R}} \).

  2. 2.

    Notice that \( \tilde{\chi }\left( {G,G} \right) = 1 \) is not required, as the alignment score has no upper bound.

  3. 3.

    Notice that the OSN similarity score measures similarity in the context of the locally aligned segments of the sequences. That is, if OSNs \( {\mathcal{G}} \) and \( {\mathcal{G}}^{'} \) have \( k \) elements aligned with average element-wise similarity of \( h \), whether \( k = min\left( {n,m} \right) \) or \( k < min\left( {n,m} \right) \), . Additionally, if OSNs \( {\mathcal{G}} \) and \( {\mathcal{G}}^{'} \) have one element aligned with element-wise similarity of 1.0, while OSNs \( {\mathcal{G}} \) and \( {\mathcal{G}}^{''} \) have four elements aligned with each element-wise similarity being 0.9, (but \( \tilde{\chi }\left( {{\mathcal{G}},{\mathcal{G}}^{\prime } } \right) < \tilde{\chi }\left( {{\mathcal{G}},{\mathcal{G}}^{\prime \prime } } \right) \)).

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Acknowledgments

This project was supported in part by the National Center for Advancing Translational Sciences, National Institutes of Health through Grant UL1 TR000127 and TR002014, by the National Science Foundation, through Grant SHF 1518732, the Center for Big Data Analytics and Discovery Informatics at Pennsylvania State University, the Edward Frymoyer Endowed Professorship in Information Sciences and Technology at Pennsylvania State University and the Sudha Murty Distinguished Visiting Chair in Neurocomputing and Data Science funded by the Pratiksha Trust at the Indian Institute of Science [both held by Vasant Honavar]. The content is solely the responsibility of the authors and does not necessarily represent the official views of the sponsors. We thank Sanghack Lee for helpful discussions during the course of this work.

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Authors and Affiliations

  1. Huck Institutes of the Life Sciences, Pennsylvania State University, University Park, PA, 16802, USA

    Shlomit Gur & Vasant G. Honavar

  2. College of Information Sciences and Technology, Pennsylvania State University, University Park, PA, 16802, USA

    Vasant G. Honavar

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  1. Shlomit Gur
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  2. Vasant G. Honavar
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Correspondence to Shlomit Gur .

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  1. Institute of Computer Vision and Applied Computer Sciences, Leipzig, Germany

    Petra Perner

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Gur, S., Honavar, V.G. (2018). PATENet: Pairwise Alignment of Time Evolving Networks. In: Perner, P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2018. Lecture Notes in Computer Science(), vol 10934. Springer, Cham. https://doi.org/10.1007/978-3-319-96136-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-96136-1_8

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