Are All Brains Wired EquallyDanai Koutra Yu Gong Joshua Vogelstein Christos 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 ① number of nodes

② number of edges

③ largest eigenvalue

④ number of triangles

⑤ number Connected components

⑥ maximum pagerank

⑦ minimum pagerank

• Vector Features ① degree distribution② pagerank distribution ③ radius distribution ④ approximate radius distribution⑤ first n-th eigenvalues distribution ⑥ Triangle distribution

Step 1: Brain Difference

FG =

…

• Connectomes of 114people• Obtained by Multimodal Magnetic Resonance Imaging• The connectomes consist of 492K-916K voxels and 9.14M-

17.42M 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 differenceThe number of edges and nodes in thegiant 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 differenceThe number of edges and nodes in thegiant 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, 2012. •Kang U, ’PEGASUS: A Peta-Scale Graph Mining System -Implementation and Observations.’, IEEE International Confer-ence on Data Mining (ICDM), Miami, Florida, USA, 2009.•Koutra D., ’DeltaCon: A Principled Massive-Graph Similar-ity Function’, SIAM International Conference in Data Mining(SDM), Austin, Texas, USA, 2013.

Brain Graph Shavving

Feature extraction

... ...

1 2 m. . .312...n

graphs

Useful features

Connectom

ics

Graphs are•unweighed •undirected

Graphs are•unweighed •undirected

analyse

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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

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1 2 d. . .312...n

graphs

the single vector feature

nxk

Ukxk

Eigenassay

uiS

si

Singular Value

kxd

vi

Eigengene

VT

u1u2

SVD

Plot out u1 VS u2

u1

u2

u1

u2

The feature cannot distinguish different groups The feature cannot distinguish different groups

Possible conclusion 1 Possible conclusion 1 distinguish different groups got distinguished on the feature distinguish different groups got distinguished on the feature

Possible conclusion 2 Possible conclusion 2

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Preliminaries

114 connectomes, groups can be divided in two ways1.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

u1 VS u2 of the matrix of the connected components distribution

The two genders differ significantly in this

feature (p-value 0.0002)

Remove the nodes or edges which may be the noise

Efficient in separating different groups

Interest sub graphs