Are All Brains Wired Equally Danai Koutra Yu GongJoshua VogelsteinChristos Faloutsos Motivation Connectomics -- creation of brain connectivity maps. Analysing the maps to understand how the brain functions. Are there differences between different people Female VS male High math skills VS normal ….. If parts of the brain are more connected Left hemisphere Right hemisphere Experimental Results Methodology CONCLUSIONS Novel approach: analyze some invariants of numerous huge brain graphs (connectomes) in order to do clustering and classification Obeservations: The size (number of edges), as well as the maximum eigenvalues of the brain graphs differ significantly between males and females. The degree distribution, and the number of tri-angles are features that can contribute towards the classification of the scans by gender. Datasets Our Approach 1 2 Scalar Features Analysis ①number of nodes ②number of edges ③largest eigenvalue ④number of triangles ⑤number Connected components ⑥maximum pagerank ⑦minimum pagerank Vector Features ①degree distribution ②pagerank distribution ③radius distribution ④approximate radius distribution ⑤first n-th eigenvalues distribution ⑥Triangle distribution Step 1: Brain Difference F G = … Connectomes of 114people Obtained by Multimodal Magnetic Resonance Imaging The connectomes consist of 492K-916K voxels and 9.14M M connections Attributes for each person(e.g., age, gender, IQ, creativity index) Each connectome is represented as unweighted undirected graph Toolkit PEGASUS Networkx Degree Distribution Observation: the extreme cases of female and male connectomes are well separated while it cannot separate connectomes with respect to to the mastery of math. Observation: the extreme cases of female and male connectomes are well separated while it cannot separate connectomes with respect to to the mastery of math. Triangles Plots Observation: Although triangle distribution don’t separate any groups. Total number of triangles succeed in females and male separation while failed for math skill separation. Observation: Although triangle distribution don’t separate any groups. Total number of triangles succeed in females and male separation while failed for math skill separation. Connected Components Observation: The connected components distributions of female and male connectomes do not have significant difference The number of edges and nodes in the giant connected component (gcc) of each brain scan, reveals two clusters corresponding to males and f-males Observation: The connected components distributions of female and male connectomes do not have significant difference The number of edges and nodes in the giant connected component (gcc) of each brain scan, reveals two clusters corresponding to males and f-males Largest Eigenvalue of Graph Matrix References Gray W., ’Magnetic resonance connectome automated pipeline:An overview’, Pulse, IEEE, vol. 3, no. 2, pp. 4248, Kang U, ’PEGASUS: A Peta-Scale Graph Mining System -Implementation and Observations.’, IEEE International Confer-ence on Data Mining (ICDM), Miami, Florida, USA, Koutra D., ’DeltaCon: A Principled Massive-Graph Similar-ity Function’, SIAM International Conference in Data Mining(SDM), Austin, Texas, USA, Brain Graph Shavving Feature extraction m n12...n graphsgraphs Useful features Connectomics Graphs are unweighed undirected Graphs are unweighed undirected analyse TODO: add pegasus and netwrokx logo here Manually divide the graphs into different groups according to labeled attributes p-value significance Plot according graphs based on #nodes to see if the groups can separate for each feature d n12...n graphsgraphs the single vector feature nxk U kxk Eigenass ay uiui S sisi Singular Value kxd vivi Eigengen e VTVT u1u1 u2u2 SVD Plot out u 1 VS u 2 u1u1 u2u2 u1u1 u2u2 The feature cannot distinguish different groups Possible conclusion 1 distinguish different groups got distinguished on the feature Possible conclusion 2 TODO: don’t know what to fill here Preliminaries 114 connectomes, groups can be divided in two ways 1.Gender 50 females are represented by red does and 64 males are represented by green dots 2.Subject Type: relates to math skills, normal, low and high math skill connectomes are represented by green red and blue dots respectively u 1 VS u 2 of the matrix of the connected components distribution The two genders differ significantly in this feature (p-value ) Remove the nodes or edges which may be the noise Efficient in separating different groups Interest sub graphs