The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.07 - July (2013 vol.35)
pp: 1539-1551
J. T. Vogelstein , Dept. of Math. & Stat., Duke Univ., Durham, NC, USA
W. G. Roncal , Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD, USA
R. J. Vogelstein , Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD, USA
C. E. Priebe , Dept. of Appl. Math. & Stat., Johns Hopkins Univ., Baltimore, MD, USA
ABSTRACT
This manuscript considers the following “graph classification” question: Given a collection of graphs and associated classes, how can one predict the class of a newly observed graph? To address this question, we propose a statistical model for graph/class pairs. This model naturally leads to a set of estimators to identify the class-conditional signal, or “signal-subgraph,” defined as the collection of edges that are probabilistically different between the classes. The estimators admit classifiers which are asymptotically optimal and efficient, but which differ by their assumption about the “coherency” of the signal-subgraph (coherency is the extent to which the signal-edges “stick together” around a common subset of vertices). Via simulation, the best estimator is shown to be not just a function of the coherency of the model, but also the number of training samples. These estimators are employed to address a contemporary neuroscience question: Can we classify “connectomes” (brain-graphs) according to sex? The answer is yes, and significantly better than all benchmark algorithms considered. Synthetic data analysis demonstrates that even when the model is correct, given the relatively small number of training samples, the estimated signal-subgraph should be taken with a grain of salt. We conclude by discussing several possible extensions.
INDEX TERMS
Pattern analysis, Joints, Neurons, Analytical models, Brain modeling, Training, Data models,classification, Statistical inference, graph theory, network theory, structural pattern recognition, connectome
CITATION
J. T. Vogelstein, W. G. Roncal, R. J. Vogelstein, C. E. Priebe, "Graph Classification Using Signal-Subgraphs: Applications in Statistical Connectomics", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.35, no. 7, pp. 1539-1551, July 2013, doi:10.1109/TPAMI.2012.235
REFERENCES
[1] H. Bunke and K. Riesen, "Towards the Unification of Structural and Statistical Pattern Recognition," Pattern Recognition Letters, vol. 33, no. 7,http://linkinghub.elsevier.com/retrieve/ pii/S0167865511001309 http://www.sciencedirect.com/ science/article/piiS0167865511001309 , pp. 811-825, May 2011.
[2] P. Hagmann, L. Cammoun, X. Gigandet, S. Gerhard, P. Ellen Grant, V. Wedeen, R. Meuli, J.-P. Thiran, C.J. Honey, and O. Sporns, "MR Connectomics: Principles and Challenges," J. Neuroscience Methods, vol. 194, no. 1,http://www.ncbi.nlm.nih. gov/entrezquery.fcgi?cmd=Retrieve&db=PubMed&dopt= Citation&list_uids=20096730 , pp. 34-45, 2010.
[3] D.L.D. Donoho, M. Elad, and V.N.V. Temlyakov, "Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise," IEEE Trans. Information Theory, vol. 52, no. 1, pp. 6-18, http://ieeexplore.ieee.org/xplarticleDetails.jsp?arnumber=1564423 , Jan. 2006.
[4] E.J. Candès and M. Wakin, "An Introduction to Compressive Sampling," IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21-30, Mar. 2008.
[5] T. Kudo, "An Application of Boosting to Graph Classification," Science.
[6] N.S. Ketkar, L.B. Holder, and D.J. Cook, "Empirical Comparison of Graph Classification Algorithms," Proc. IEEE Symp. Computational Intelligence and Data Mining, pp. 259-266, http://ieeexplore.ieee.org/lpdocs/epic03 wrapper.htm?arnumber= 4938658, Mar. 2009.
[7] G. North, Invertebrate Neurobiology, R.J.G. Geoffrey North, ed. CSHL Press, 2007.
[8] J.D. Shepherd and R.L. Huganir, "The Cell Biology of Synaptic Plasticity: AMPA Receptor Trafficking," Ann. Rev. Cell and Developmental Biology, vol. 23, pp. 613-643, http://www.ncbi.nlm.nih.gov/pubmed17506699 , Jan. 2007.
[9] J. Nolte, The Human Brain: An Introduction to Its Functional Anatomy. Mosby, 2002.
[10] J.W. Lichtman, J. Livet, and J.R. Sanes, "A Technicolour Approach to the Connectome," Nature Rev. Neuroscience, vol. 9, no. 6, pp. 417-422, http://dx.doi.org/10.1038nrn2391, June 2008.
[11] D.S. Bassett and E.T. Bullmore, "Human Brain Networks in Health and Disease," Current Opinion in Neurology, vol. 22, no. 4, pp. 340-347, 2009.
[12] J. Lasserre, C.M. Bishop, and T. Minka, "Principled Hybrids of Generative and Discriminative Models," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 87-94, http://ieeexplore.ieee.org/lpdocs/epic03 wrapper.htm?arnumber= 1640745, 2006.
[13] P.J. Bickel and K.A. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, vol. 1, second ed. Prentice Hall, 2000.
[14] C.M. Stein, "Inadmissibility of the Usual Estimator of the Mean of a Multivariate Normal Distribution," Proc. Third Berkeley Symp. Math. Statistics and Probability, pp. 197-206, 1956.
[15] P.I. Good, Permutation, Parametric, and Bootstrap Tests of Hypotheses. Springer, 2010.
[16] Q. McNemar, "Note on the Sampling Error of the Difference between Correlated Proportions or Percentages," Psychometrika, vol. 12, no. 2, pp. 153-157, June 1947.
[17] P.J. Huber, Robust Statistics. Wiley, http://doi.wiley.com/10.10029780470434697 , 1981.
[18] J.A. Rice, Mathematical Statistics and Data Analysis. Duxbury Press, 1995.
[19] D.J. Hand and K. Yu, "Idiot's Bayes: Not So Stupid After All?" Int'l J. Statistical Rev., vol. 69, no. 3, pp. 385-398, Nov. 2001.
[20] R. Tibshirani, "Regression Shrinkage and Selection via the Lasso," J. Royal Statistical Soc., Series B, vol. 58, pp. 267-288, 1996.
[21] B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, "Least Angle Regression," Annals of Statistics, vol. 32, no. 2, pp. 407-499, 2004.
[22] A.K. Jain, R.P.W. Duin, J. Mao, and S. Member, "Statistical Pattern Recognition: A Review," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 1, pp. 4-37, http://ieeexplore.ieee.org/lpdocs/epic03 wrapper.htm?arnumber=824819, Jan. 2000.
[23] O. Sporns, Networks of the Brain. The MIT Press, 2010.
[24] J.T. Vogelstein, W.R. Gray, J.L. Prince, L. Ferrucci, S.M. Resnick, C.E. Priebe, and R.J. Vogelstein, "Graph-Theoretical Methods for Statistical Inference on MR Connectome Data," Organization Human Brain Mapping, 2010.
[25] W.R. Gray, J.A. Bogovic, J.T. Vogelstein, B.A. Landman, J.L. Prince, and R.J. Vogelstein, "Magnetic Resonance Connectome Automated Pipeline: An Overview." IEEE Pulse, vol. 3, no. 2, pp. 42-48, http://ieeexplore.ieee.org/xplarticleDetails.jsp? arnumber=6173097 , Mar. 2010.
[26] J.T. Vogelstein, R.J. Vogelstein, and C.E. Priebe, "Are Mental Properties Supervenient on Brain Properties?" Nature Scientific Reports, p. 11, 2011.
[27] H. Pao, G.A. Coppersmith, C.E. Priebe, H.P. Ao, G.A.C. Oppersmith, and C.E.P. Riebe, "Statistical Inference on Random Graphs: Comparative Power Analyses via Monte Carlo," J. Computational and Graphical Statistics, 20, pp. 1-22, http://pubs.amstat.org/doi/abs/10.1198jcgs.2010.09004 , 2010.
[28] C.E. Priebe, G.A. Coppersmith, and A. Rukhin, "You Say Graph Invariant, I Say Test Statistic," Statistical Computing Statistical Graphics Newsletter, vol. 21, no. 2, pp. 11-14, 2010.
[29] A. Rukhin and C.E. Priebe, "A Comparative Power Analysis of the Maximum Degree and Size Invariants for Random Graph Inference," J. Statistical Planning and Inference, vol. 141, no. 2, pp. 1041-1046, 2011.
[30] I.S. Dhillon, "Co-Clustering Documents and Words Using Bipartite Spectral Graph Partitioning," Proc. Seventh ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining, pp. 269-274, http://portal.acm.orgcitation.cfm?doid=502512.502550 , 2001.
[31] L. Devroye, L. Györfi, G. Lugosi, and L. Gyorfi, A Probabilistic Theory of Pattern Recognition. Springer, 1996.
[32] E.J. Candès and B. Recht, "Exact Matrix Completion via Convex Optimization," Foundations of Computational Math., vol. 9, no. 6, pp. 717-772, Apr. 2009.
[33] X. Ding, L. He, and L. Carin, "Bayesian Robust Principal Component Analysis," Image, vol. 20, no. 12, pp. 3419-3430, 2011.
[34] V. Chandrasekaran, S. Sanghavi, P.A. Parrilo, and A.S. Willsky, "Rank-Sparsity Incoherence for Matrix Decomposition," SIAM J. Optimization, vol. 21, no. 2, p. 572, June 2011.
[35] P.D. Hoff, A.E. Raftery, and M.S. Handcock, "Latent Space Approaches to Social Network Analysis," J. Am. Statistical Assoc., vol. 97, no. 460, pp. 1090-1098, http://pubs.amstat.org/doi/abs/10.1198016214502388618906 , Dec. 2002.
[36] D.L. Sussman, M. Tang, D.E. Fishkind, and C.E. Priebe, "A Consistent Dot Product Embedding for Stochastic Blockmodel Graphs," J. Am. Statistical Assoc., p. 17, 2012.
[37] D.E. Fishkind, D.L. Sussman, M. Tang, J.T. Vogelstein, and C.E. Priebe, "Consistent Adjacency-Spectral Partitioning for the Stochastic Block Model When the Model Parameters Are Unknown," Rapid Post, http://arxiv.org/abs1205.0309, p. 20, May 2012.
[38] J.T. Vogelstein, J.C.M. Conroy, L.J. Podrazik, S.G. Kratzer, D.E. Fishkind, R.J. Vogelstein, and C.E. Priebe, "(Brain) Graph Matching via Fast Approximate Quadratic Programming," Rapid Post, 2011.
[39] J.T. Vogelstein and C.E. Priebe, "Shuffled Graph Classification: Theory and Connectome Applications," arXiv:1112.5506v2 [q-bio.QM], 2011.
[40] G.A. Coppersmith and C.E. Priebe, "Vertex Nomination via Content and Context," Technology, pp. 1-21, 2012.
[41] D.J. Marchette, C.E. Priebe, and G.A. Coppersmith, "Vertex Nomination via Attributed Random Dot Product Graphs," 2011.
[42] D.S. Lee and C.E. Priebe, "Bayesian Vertex Nomination," Rapid Post, 2012.
[43] D.D. Bock, W.-C.A. Lee, A.M. Kerlin, M.L. Andermann, A.W. Wetzel, S. Yurgenson, E.R. Soucy, H.S. Kim, G. Hood, and R.C. Reid, "Network Anatomy and in Vivo Physiology of Visual Cortical Neurons," Nature, vol. 471, no. 7337, pp. 177-182, Mar. 2011.
17 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool