Are All Brains Wired Equally Danai Koutra Yu GongJoshua VogelsteinChristos Faloutsos Motivation...
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Are All Brains Wired Equally Danai 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 distribution ② pagerank distribution ③ radius distribution ④ approximate radius distribution ⑤ first n-th eigenvalues distribution ⑥ Triangle 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-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 . 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. 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 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 . . . 3 1 2 . . . n g r a p h s Useful features Connectomi cs Graphs are •unweighed •undirected analy se 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 ... ... 1 2 d . . . 3 1 2 . . . n g r a p h s the single vector feature nxk U kxk Eigenas say u i S s i Singular Value kxd v i Eigenge ne V T u 1 u 2 SVD Plot out u 1 VS u 2 u 1 u 2 u 1 u 2 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 0.0002) Remove the nodes or edges which may be the noise Efficie nt in separat ing differe nt groups Inter est sub graph s
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Transcript of Are All Brains Wired Equally Danai Koutra Yu GongJoshua VogelsteinChristos Faloutsos Motivation...
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
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
... ...
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
TODO: don’t know what to fill here
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
