ABSTRACT
Block models of graphs are used in a wide variety of domains as they find not only clusters (the blocks) but also interaction within and between the blocks. However, existing approaches primarily focus on either structural graphs (i.e. for MRI scans) or behavioral graphs (i.e. for fMRI scans). In both cases the block model's interaction or mixing matrix can be useful for understanding potential interaction (for structural graphs) and actual interaction (for behavioral graphs) between the blocks. In this paper we explore finding block models where there is both a structural network and multiple behavioral graphs. This provides significant modeling challenges, consider if there is strong behavioral connectivity but no structural connectivity between two nodes. We show why existing multi-graph settings such as multi-view learning are insufficient and instead propose a novel model to address the problem. Our method not only learns structurally and behaviorally cohesive blocks of nodes but also finds structurally and behaviorally feasible block interactions. We show in numerical evaluations on synthetic data that our method outperforms baseline approaches in recovering the ground-truth factor matrices in increasingly complex situations. We further apply our method to real-world datasets from two different domains (1) brain imaging data (a multi-cohort fMRI study) and to show its versatility (2) Twitter (following network and retweet behavior) and gain insights into the information flow and underlying generating mechanisms of these complex data.
- Christopher Aicher, Abigail Z Jacobs, and Aaron Clauset. 2014. Learning latent block structure in weighted networks. Journal of Complex Networks 3, 2 (2014), 221--248.Google ScholarCross Ref
- RB Arango, AM Campos, Elías F Combarro, ER Canas, and Irene Díaz. 2016. Mapping cultivable land from satellite imagery with clustering algorithms. International Journal of Applied Earth Observation and Geoinformation 49 (2016), 99--106.Google ScholarCross Ref
- Zilong Bai, Peter Walker, and Ian Davidson. 2018. Mixtures of Block Models for Brain Networks. In Proceedings of the 2018 SIAM International Conference on Data Mining. SIAM, 46--54.Google ScholarCross Ref
- Zilong Bai, Peter Walker, Anna Tschiffely, Fei Wang, and Ian Davidson. 2017. Unsupervised Network Discovery for Brain Imaging Data. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD '17). ACM, New York, NY, USA, 55--64. Google ScholarDigital Library
- Vincent D Blondel, Jean-Loup Guillaume, Renaud Lambiotte, and Etienne Lefebvre. 2008. Fast unfolding of communities in large networks. Journal of statistical mechanics: theory and experiment 2008, 10 (2008), P10008.Google ScholarCross Ref
- Chris Ding, Tao Li, Wei Peng, and Haesun Park. 2006. Orthogonal Nonnegative Matrix T-factorizations for Clustering. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD '06). ACM, New York, NY, USA, 126--135. Google ScholarDigital Library
- Patric Hagmann, Maciej Kurant, Xavier Gigandet, Patrick Thiran, Van J Wedeen, Reto Meuli, and Jean-Philippe Thiran. 2007. Mapping human whole-brain structural networks with diffusion MRI. PloS one 2, 7 (2007), e597.Google ScholarCross Ref
- Hisashi Kashima, Koji Tsuda, and Akihiro Inokuchi. 2003. Marginalized kernels between labeled graphs. In Proceedings of the 20th international conference on machine learning (ICML-03). 321--328. Google ScholarDigital Library
- Daniel D. Lee and H. Sebastian Seung. 2001. Algorithms for Non-negative Matrix Factorization. In Advances in Neural Information Processing Systems 13, T. K. Leen, T. G. Dietterich, and V. Tresp (Eds.). MIT Press, 556--562. http://papers.nips.cc/ paper/1861-algorithms-for-non-negative-matrix-factorization.pdfGoogle Scholar
- Andrew Y Ng, Michael I Jordan, and Yair Weiss. 2002. On spectral clustering: Analysis and an algorithm. In Advances in neural information processing systems. 849--856. Google ScholarDigital Library
- Maximilian Nickel, Volker Tresp, and Hans-Peter Kriegel. 2011. A Three-way Model for Collective Learning on Multi-relational Data. In Proceedings of the 28th International Conference on International Conference on Machine Learning (ICML'11). Omnipress, USA, 809--816. http://dl.acm.org/citation.cfm?id=3104482. 3104584 Google ScholarDigital Library
- S. Paul and Y. Chen. 2016. Orthogonal symmetric non-negative matrix factorization under the stochastic block model. ArXiv e-prints (May 2016). arXiv:stat.ML/1605.05349Google Scholar
- J. Qiu, J. Peng, and Y. Zhai. 2014. Network community detection based on spectral clustering. In 2014 International Conference on Machine Learning and Cybernetics, Vol. 2. 648--652.Google Scholar
- Yonggang Shi and Arthur W Toga. 2017. Connectome imaging for mapping human brain pathways. Molecular psychiatry 22, 9 (2017), 1230.Google Scholar
- Olaf Sporns. 2013. Structure and function of complex brain networks. Dialogues in clinical neuroscience 15, 3 (2013), 247.Google Scholar
- W. Tang, Z. Lu, and I. S. Dhillon. 2009. Clustering with Multiple Graphs. In 2009 Ninth IEEE International Conference on Data Mining. 1016--1021. Google ScholarDigital Library
- Nathalie Tzourio-Mazoyer, Brigitte Landeau, Dimitri Papathanassiou, Fabrice Crivello, Olivier Etard, Nicolas Delcroix, Bernard Mazoyer, and Marc Joliot. 2002. Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 15, 1 (2002), 273--289.Google ScholarCross Ref
- Kun Wang, Meng Liang, Liang Wang, Lixia Tian, Xinqing Zhang, Kuncheng Li, and Tianzi Jiang. 2007. Altered functional connectivity in early Alzheimer's disease: a resting-state fMRI study. Human brain mapping 28, 10 (2007), 967--978.Google Scholar
- Xiang Wang, Buyue Qian, Jieping Ye, and Ian Davidson. 2013. Multi-objective multi-view spectral clustering via pareto optimization. In Proceedings of the 2013 SIAM International Conference on Data Mining. SIAM, 234--242.Google ScholarCross Ref
- J. Yang, J. McAuley, and J. Leskovec. 2013. Community Detection in Networks with Node Attributes. In 2013 IEEE 13th International Conference on Data Mining. 1151--1156.Google Scholar
- Zhong-Yuan Zhang, Yujie Gai, Yu-Fei Wang, Hui-Min Cheng, and Xin Liu. 2018. On equivalence of likelihood maximization of stochastic block model and constrained nonnegative matrix factorization. Physica A: Statistical Mechanics and its Applications 503 (2018), 687--697.Google Scholar
- Dengyong Zhou and Christopher J. C. Burges. 2007. Spectral Clustering and Transductive Learning with Multiple Views. In Proceedings of the 24th International Conference on Machine Learning (ICML '07). ACM, New York, NY, USA, 1159--1166. Google ScholarDigital Library
Index Terms
- Discovering Models from Structural and Behavioral Brain Imaging Data
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