UCLA UCLA Electronic Theses and Dissertations Title Bipartite Network Community Detection: Development and Survey of Algorithmic and Stochastic Block Model Based Methods Permalink https://escholarship.org/uc/item/0tr9j01r Author Sun, Yidan Publication Date 2021 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA Los Angeles Bipartite Network Community Detection: Development and Survey of Algorithmic and Stochastic Block Model Based Methods A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Statistics by Yidan Sun 2021 © Copyright by Yidan Sun 2021 ABSTRACT OF THE DISSERTATION Bipartite Network Community Detection: Development and Survey of Algorithmic and Stochastic Block Model Based Methods by Yidan Sun Doctor of Philosophy in Statistics University of California, Los Angeles, 2021 Professor Jingyi Li, Chair In a bipartite network, nodes are divided into two types, and edges are only allowed to connect nodes of different types. Bipartite network clustering problems aim to identify node groups with more edges between themselves and fewer edges to the rest of the network. The approaches for community detection in the bipartite network can roughly be classified into algorithmic and model-based methods. The algorithmic methods solve the problem either by greedy searches in a heuristic way or optimizing based on some criteria over all possible partitions. The model-based methods fit a generative model to the observed data and study the model in a statistically principled way. In this dissertation, we mainly focus on bipartite clustering under two scenarios: incorporation of node covariates and detection of mixed membership communities. In Chapter 2, we study an algorithmic bipartite clustering method in the context of gene co-clustering. Gene co-clustering is a widely-used technique that has enabled computational prediction of unknown gene functions within a species. However, it remains a challenge to refine gene function prediction by leveraging evolutionarily conserved genes in another species. This challenge calls for a new computational algorithm to identify gene co-clusters in two species, so that genes in each co-cluster exhibit similar expression levels in each species and strong conservation between the species. Here we develop the bipartite tight ii spectral clustering (BiTSC) algorithm, which identifies gene co-clusters in two species based on gene orthology information and gene expression data. BiTSC novelly implements a formulation that encodes gene orthology as a bipartite network and gene expression data as node covariates. This formulation allows BiTSC to adopt and combine the advantages of multiple unsupervised learning techniques: kernel enhancement, bipartite spectral clustering, consensus clustering, tight clustering, and hierarchical clustering. As a result, BiTSC is a flexible and robust algorithm capable of identifying informative gene co-clusters without forcing all genes into co-clusters. Another advantage of BiTSC is that it does not rely on any distributional assumptions. Beyond cross-species gene co-clustering, BiTSC also has wide applications as a general algorithm for identifying tight node co-clusters in any bipartite network with node covariates. We demonstrate the accuracy and robustness of BiTSC through comprehensive simulation studies. In a real data example, we use BiTSC to identify conserved gene co-clusters of D. melanogaster and C. elegans, and we perform a series of downstream analyses to both validate BiTSC and verify the biological significance of the identified co-clusters. The stochastic block model (SBM) serves as a fundamental and classic tool to study model- based community detection in a statistically principled way. It is a simple generative model but too restrictive to include empirical network characteristics. With the flexibility of the SBM, many SBM variants have been proposed to accommodate the real-world scenarios, such as node degree heterogeneity, mixed membership communities, and bipartite structure. In Chapter 3, we review a few extensions of the SBM, including degree-correction SBM, mixed membership SBM, and bipartite SBM. We conduct a survey about community detection methods based on the mixed membership SBM and bipartite SBM. We discuss these methods in detail and summarize the challenges in introducing degree-correction to the mixed membership SBM; the challenges in extending the degree-corrected mixed membership SBM to the bipartite network. To address some of the research gaps discussed in Chapter 3, we construct a generative bipartite degree-corrected mixed membership SBM in Chapter 4. To fit the model, we iii propose a variational expectation-maximization (EM) algorithm. We perform a preliminary simulation study in which the result suggests that the algorithm is sensitive to the initial values. We discuss the possible improvements for future directions. iv The dissertation of Yidan Sun is approved. Mark Stephen Handcock Yingnian Wu Sriram Sankararaman Jingyi Li, Committee Chair University of California, Los Angeles 2021 v To my mom and dad. vi TABLE OF CONTENTS List of Figures ...................................... x List of Tables ....................................... xii Acknowledgments .................................... xiii Vita ............................................. xiv 1 Introduction ...................................... 1 1.1 Background and Motivation . .1 1.2 Outline . .6 2 Bipartite Tight Spectral Clustering (BiTSC) Algorithm .......... 7 2.1 Introduction . .7 2.2 Methods . 10 2.2.1 Bipartite network formulation . 10 2.2.2 The BiTSC algorithm . 11 2.2.3 Six possible variants . 17 2.3 Results . 19 2.3.1 Simulation . 19 2.3.2 Real data analysis . 23 2.3.3 Bioinformatics gene function analysis . 31 2.4 Discussion . 34 2.5 Acknowledgments . 36 vii Appendices ........................................ 37 2.A Code . 37 2.B Evaluation metric of clustering result . 37 2.C Robustness analysis of input parameters . 38 2.D Choice of K0 in the real data application . 40 2.E Computational time . 41 3 A Survey of Mixed Membership SBMs and Bipartite SBMs ....... 56 3.1 Introduction . 56 3.2 Simple SBM . 58 3.3 Degree-correction SBM . 59 3.4 Mixed membership SBM . 61 3.5 Bipartite SBM . 67 3.6 Summary and discussion . 69 3.7 Acknowledgements . 70 4 A Bipartite Mixed Membership Stochastic Block Model .......... 72 4.1 Model . 72 4.2 Model fitting and variational EM algorithm . 75 4.2.1 Variational E step . 78 4.2.2 Variational M step . 80 4.2.3 Parameter estimation . 83 4.3 Preliminary simulation study . 85 4.4 Conclusion and future work . 87 4.5 Code . 90 viii 4.6 Acknowledgements . 90 Appendices ........................................ 92 4.A Details of updating φ ............................... 92 4.B Details of updating θ ............................... 92 4.B.1 Definitions . 93 4.B.2 Douglas-Rachford splitting method . 94 4.C The power law and the Pareto distribution . 94 5 Discussion ....................................... 96 Bibliography ....................................... 97 ix LIST OF FIGURES 2.1 Diagram illustrating the input and output of BiTSC . 11 2.2 Performance of BiTSC vs. (a) its six variant algorithms and (b) OrthoClust . 24 2.3 Comparison of BiTSC and OrthoClust in terms of their identified fly-worm gene co-clusters . 26 2.4 Visualization of the 16 gene co-clusters found by BiTSC from the fly-worm gene network . 30 2.5 Performance of BiTSC vs. OrthoClust . 41 2.6 Top five enriched BP GO terms in each of the 16 fly-worm gene co-clusters identified by BiTSC . 42 2.7 Boxplots of pairwise Pearson correlation coefficients in each species within each of the 16 fly-worm gene co-clusters identified by BiTSC . 43 2.8 Workflow of BiTSC . 44 2.9 The simulated bipartite network example . 45 2.10 Clustering performance of BiTSC and three variant algorithms as functions of K0, ρ and τ ........................................ 46 2.11 Clustering performance of BiTSC and three variant algorithms as functions of τ 47 2.12 Choice of K0 ..................................... 50 2.13 Robustness of the random selection of 1,000 unclustered genes . 52 2.14 MF and CC GO terms of the genes without BP GO terms in the 16 gene co-clusters identified by BiTSC . 53 2.15 Comparison of BiTSC and OrthoClust in terms of their identified co-clusters . 54 2.16 Comparison of BiTSC and OrthoClust in terms of link prediction performance on the fly-worm data set . 55 x 4.1 A diagram of the generative bipartite degree-corrected mixed membership stochastic block model. 75 4.2 The diagram of the variational distribution. 78 4.3 The simulation results in the non-degree-correction scenario. 88 4.4 The simulation results in the degree-correction scenario. 89 xi LIST OF TABLES 2.1 Fly-worm gene co-clusters identified by BiTSC . 29 2.2 Fly-worm gene co-clusters identified by OrthoClust (Section 2.3.2) . 48 2.3 Fly-worm gene co-clusters identified by OrthoClust (Section 2.3.2) . 49 3.1 List of (degree-corrected) mixed membership stochastic block models and (degree- corrected) bipartite stochastic block models. 71 xii ACKNOWLEDGMENTS I would like to thank my advisor Prof. Jingyi Jessica Li for the continuous support, help, patience, encouragement, and career guidance throughout my graduate study. I owe the successful completion of my thesis to her. I would not be where I am today without her help. I would like to thank my committee members, Prof. Mark Handcock, Prof. Yingnian Wu and Prof. Sriram Sankararaman, for their insightful suggestions and discussions on my dissertation. Special thanks to Prof. Mark Handcock, Prof. Nicolas Christou and Prof. Xin Tong, for their help in career guidance. I would like to thank my co-author Heather Zhou for the generous help. I would like to thank my friends, Kexin Li, Wei Li, Wenbin Guo, Ruochen Jiang, Dongyuan Song, Nan Xi, Guan’ao Yan, Yucheng Yang, Kun Zhou, Zhixin Zhou, and all the other members in the Junction of Statistics and Biology (http://jsb.ucla.edu), for their continuous support and encouragement. xiii VITA 2011 - 2015 B.S. in Mathematical Finance, Wuhan University 2015 - 2021 Ph.D.