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Issue No.12 - Dec. (2012 vol.18)
pp: 2457-2466
ABSTRACT
We present a novel technique-Compressed Adjacency Matrices-for visualizing gene regulatory networks. These directed networks have strong structural characteristics: out-degrees with a scale-free distribution, in-degrees bound by a low maximum, and few and small cycles. Standard visualization techniques, such as node-link diagrams and adjacency matrices, are impeded by these network characteristics. The scale-free distribution of out-degrees causes a high number of intersecting edges in node-link diagrams. Adjacency matrices become space-inefficient due to the low in-degrees and the resulting sparse network. Compressed adjacency matrices, however, exploit these structural characteristics. By cutting open and rearranging an adjacency matrix, we achieve a compact and neatly-arranged visualization. Compressed adjacency matrices allow for easy detection of subnetworks with a specific structure, so-called motifs, which provide important knowledge about gene regulatory networks to domain experts. We summarize motifs commonly referred to in the literature, and relate them to network analysis tasks common to the visualization domain. We show that a user can easily find the important motifs in compressed adjacency matrices, and that this is hard in standard adjacency matrix and node-link diagrams. We also demonstrate that interaction techniques for standard adjacency matrices can be used for our compressed variant. These techniques include rearrangement clustering, highlighting, and filtering.
INDEX TERMS
network theory (graphs), biology computing, data visualisation, genetics, matrix algebra, rearrangement clustering, compressed adjacency matrices, gene regulatory networks, directed networks, structural characteristics, scale-free distribution, standard visualization, node-link diagrams, network characteristics, sparse network, neatly-arranged visualization, motifs, visualization domain, standard adjacency matrix, Visualization, Computer aided manufacturing, Standards, Sparse matrices, Layout, Bismuth, Proteins, adjacency matrix, Network, gene regulation, scale-free
CITATION
K. Dinkla, M. A. Westenberg, J. J. van Wijk, "Compressed Adjacency Matrices: Untangling Gene Regulatory Networks", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 12, pp. 2457-2466, Dec. 2012, doi:10.1109/TVCG.2012.208
REFERENCES
[1] J. Abello and F. van Ham., Matrix Zoom: A visual interface to semi-external graphs. In IEEE Proc. Symposium on Information Visualization, pages 183-190, 2004.
[2] U. Alon., An Introduction to Systems Biology: Design Principles of Biological Circuits. CRC press, 2006.
[3] R. Andersen, F. Chung, and L. Lu, Drawing power law graphs using a local/global decomposition Algorithmica. 47(4): 379-397, 2007.
[4] D. Archambault, T. Munzner, and D. Auber, GrouseFlocks: Steerable ex-ploration of graph hierarchy space IEEE Trans. Visualization and Computer Graphics, 14(4): 900-913, 2008.
[5] G. Battista, P. Eades, R. Tamassia,, and I. Tollis., Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall PTR, 1998.
[6] A. Bezerianos, P. Dragicevic, J.-D. Fekete, J. Bae, and B. Watson, Ge-neaQuilts: A system for exploring large genealogies IEEE Trans. Visualization and Computer Graphics, 16(6): 1073-1081, 2010.
[7] K. Boitmanis, U. Brandes, and C. Pich., Visualizing internet evolution on the autonomous systems level. In Graph Drawing, 4875 of Lecture Notes in Computer Science, pages 365-376. Springer Berlin / Heidelberg, 2008.
[8] D. Croft,G. O’Kelly, G. Wu, R. Haw, M. Gillespie, L. Matthews, M. Caudy, P. Garapati, G. Gopinath, B. Jassal, S. Jupe, I. Kalatskaya, S. Mahajan, B. May, N. Ndegwa, E. Schmidt, V. Shamovsky, C. Yung, E. Birney, H. Hermjakob,P. D’Eustachio,, and L. Stein., Reactome: A database of reactions, pathways and biological processes. Nucleic Acids Research, 39(suppl 1):D691–D697, 2011.
[9] W. Didimo, G. Liotta, and S. Romeo, Topology-driven force-directed al-gorithms In Graph Drawing, 6502 of Lecture Notes in Computer Science, pages 165-176. Springer Berlin / Heidelberg, 2011.
[10] T. Dwyer, Y. Koren, and K. Marriott, Ipsep-cola: An incremental procedure for separation constraint layout of graphs IEEE Trans. Visualization and Computer Graphics, 12(5): 821-828, 2006.
[11] P. Eades, A heuristic for graph drawing Congressus Numerantium, 42: 149-160, 1984.
[12] N. Elmqvist, T. Do, H. Goodell, N. Henry, and J.-D. Fekete., Zame: Interactive large-scale graph visualization. In IEEE Proc. Pacific Visualization Symposium, pages 215-222, 2008.
[13] T. Fruchterman and E. Reingold, Graph drawing by force-directed place-ment Software: Practice and Experience, 21(11): 1129-1164, 1991.
[14] M. Ghoniem, J.-D. Fekete, and P. Castagliola., A comparison of the readability of graphs using node-link and matrix-based representations. In IEEE Proc. Symposium on Information Visualization, pages 17-24, 2004.
[15] M. Graham and J. Kennedy, Exploring multiple trees through DAG representations IEEE Trans. Visualization and Computer Graphics, 13(6): 1294-1301, 2007.
[16] M. Graham, J. Kennedy, T. Paterson,, and A. Law., Visualising errors in animal pedigree genotype data. Computer Graphics Forum, 30(3): 1011-1020, 2011.
[17] D. Harel and Y. Koren., A fast multi-scale method for drawing large graphs. In Graph Drawing, 1984 of Lecture Notes in Computer Science, pages 235-287. Springer Berlin / Heidelberg, 2001.
[18] J. Heer and D. Boyd., Vizster: Visualizing online social networks. In IEEE Proc. Symposium on Information Visualization, pages 32-39, 2005.
[19] N. Henry, A. Bezcrianos, and J.-D. Fekete, Improving the readability of clustered social networks using node duplication IEEE Trans. Visualization and Computer Graphics, 14(6): 1317-1324, 2008.
[20] N. Henry and J.-D. Fekete, MatrixExplorer: a dual-representation system to explore social networks IEEE Trans. Visualization and Computer Graphics, 12(5): 677-684, 2006.
[21] N. Henry, J.-D. Fekete, and M. McGuffin, NodeTrix: a hybrid visualization of social networks IEEE Trans. Visualization and Computer Graphics, 13(6): 1302-1309, 2007.
[22] I. Herman, G. Melancon, and M. Marshall, Graph visualization and nav-igation in information visualization: A survey IEEE Trans. Visualization and Computer Graphics, 6(1): 24-43, 2000.
[23] D. Holten, Hierarchical edge bundles: Visualization of adjacency re-lations in hierarchical data IEEE Trans. Visualization and Computer Graphics, 12(5): 741-748, 2006.
[24] Z. Hu, D. Ng, T. Yamada, C. Chen, S. Kawashima, J. Mellor, B. Linghu, M. Kanehisa, J. Stuart,, and C. DeLisi., VisANT 3.0: New modules for pathway visualization, editing, prediction and construction. Nucleic Acids Research, 35(suppl 2):W625–W632, 2007.
[25] Juhee Bae and B. Watson., Developing and evaluating quilts for the depiction of large layered graphs. IEEE Trans. Visualization and Computer Graphics, 17(12): 2268-2275, 2011.
[26] G. Kerr, H. Ruskin, M. Crane,, and P. Doolan., Techniques for clustering gene expression data. Computers in Biology and Medicine, 38(3): 283-293, 2008.
[27] G. Klau and P. Mutzel., Optimal compaction of orthogonal grid drawings. In Integer Programming and Combinatorial Optimization, 1610 of Lecture Notes in Computer Science, pages 304-319. Springer Berlin / Heidelberg, 1999.
[28] S. Kozhenkov, Y. Dubinina, M. Sedova, A. Gupta, J. Ponomarenko,, and M. Baitaluk., BiologicalNetworks 2.0 – an integrative view of genome biology data. BMC Bioinformatics, 11(1): 610, 2010.
[29] B. Lee, C. Plaisant, C. Parr, J.-D. Fekete, and N. Henry., Task taxonomy for graph visualization. In Proc. AVI Workshop on Beyond Time and Errors: Novel Evaluation Methods for Information Visualization, BELIV ‘06, pages 1-5. ACM, 2006.
[30] Y. Makita, M. Nakao, N. Ogasawara,, and K. Nakai., DBTBS: Database of transcriptional regulation in Bacillus subtilis and its contribution to comparative genomics. Nucleic Acids Research, 32(suppl 1):D75–D77, 2004.
[31] L. Matthews, G. Gopinath, M. Gillespie, M. Caudy, D. Croft,B. de Bono, P. Garapati, J. Hemish, H. Hermjakob, B. Jassal, A. Kanapin, S. Lewis, S. Mahajan, B. May, E. Schmidt, I. Vastrik, G. Wu, E. Birney, L. Stein, and P. DEustachio, Reactome knowledgebase of human biological pathways and processes Nucleic Acids Research, 37(suppl 1):D619–D622, 2009.
[32] W. McCormick, P. Schweitzer, and T. White, Problem decomposition and data reorganization by a clustering technique Operations Research, 20(5): 993-1009, 1972.
[33] M. Meyer, B. Wong, M. Styczynski, T. Munzner, and H. Pfister, Pathline: A tool for comparative functional genomics Computer Graphics Forum, 29(3): 1043-1052, 2010.
[34] E. Reingold and J. Tilford, Tidier drawings of trees IEEE Trans. Software Engineering, SE- 7(2): 223-228, March 1981.
[35] L. Royer, M. Reimann, B. Andreopoulos,, and M. Schroeder., Unraveling protein networks with power graph analysis. PLoS Computational Biology, 4(7): e1000108, 2008.
[36] H. Salgado,S. Gama-Castro,M. Peralta-Gil,E. Daz-Peredo,F. Snchez-Solano,A. Santos-Zavaleta,I. Martnez-Flores,V. Jimnez-Jacinto,C. Bonavides-Martnez,J. Segura-Salazar,A. Martnez-Antonio,J. Collado-Vides,, and J. Collado-Vides., RegulonDB (version 5.0): K-12 transcriptional regulatory network, operon organization, and growth conditions. Nucleic Acids Research, 34(suppl 1): D394-D397, 2006.
[37] P. Saraiya, C. North, and K. Duca., An evaluation of microarray visualization tools for biological insight. In IEEE Proc. Symposium on Information Visualization, pages 1-8, 2004.
[38] P. Shannon, A. Markiel, O. Ozier, N. Baliga, J. Wang, D. Ramage, N. Amin, B. Schwikowski, and T. Ideker, Cytoscape: A software en-vironment for integrated models of biomolecular interaction networks Genome Research, 13(11): 2498-2504, 2003.
[39] P. Simonctto, D. Archambault, D. Auber,, and R. Bourqui., ImPrEd: An improved force-directed algorithm that prevents nodes from crossing edges. Computer Graphics Forum, 30(3): 1071-1080, 2011.
[40] K. Sugiyama, S. Tagawa, and M. Toda, Methods for visual understanding of hierarchical system structures IEEE Trans. Systems, Man and Cyber-netics, 11(2): 109-125, 1981.
[41] F. van Ham., Using multilevel call matrices in large software projects. In IEEE Proc. Symposium on Information Visualization, pages 227-232, 2003.
[42] T. von Landesberger, A. Kuijper, T. Schreck, J. Kohlhammer, J. van Wijk, J.-D. Fekete, and D. Fellner, Visual analysis of large graphs: State-of-the-art and future research challenges Computer Graphics Forum, 30(6): 1719-1749, 2011.
[43] M. Westenberg,S. van Hijum, O. Kuipers, and J. Roerdink, Visualizing genome expression and regulatory network dynamics in genomic and metabolic context Computer Graphics Forum, 27(3): 887-894, 2008.
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