This document summarizes research analyzing brain networks using diffusion tensor imaging (DTI) data. Three methods were used to select significant edges in DTI graphs: Borda ranking with strong/weak ties filtering, t-test with strong/weak ties filtering, and t-test with strong ties only. A propagation model was defined to simulate information spreading. Community detection was performed using spectral clustering and Infomap algorithms. Results showed stable communities were detected and information propagation needs further improvement.

1. DTI brain networks analysis
Significativity, propagation and community detection
Emanuele Pesce, Alessandro Merola
Neural Network and Knowledge Discovery
Università degli studi di Salerno
July 2015

2. Preprocessing
Borda + strong/weak ties
T-test + strong/weak ties
T-test + Strong ties
Propagation
Model
Example
Results
Community detection
Spectral clustering
Spectral clustering results
Infomap
Infomap results
Mutual information
Conclusions

3. Contents
Preprocessing
Borda + strong/weak ties
T-test + strong/weak ties
T-test + Strong ties
Propagation
Model
Example
Results
Community detection
Spectral clustering
Spectral clustering results
Infomap
Infomap results
Mutual information
Conclusions

4. Input Dataset
70 subjects
20 controls
50 patients (SLA)
DTI data
90 regions of interest (ROI)

5. Graphs
Modelling the problem with graphs
Each graph has 90 vretices and 8100 edges (full connected)
The weight of an edge stands for the number of streamline
between two brain areas

6. Choosing significant edges
There is the need of ”pruning” the edges, removing those less
significant and keeping the most important ones
Three ways:
Borda + strong/weak ties
T-test + strong/weak ties
T-test + strong ties

7. Borda + strong/weak ties
Borda counting
The idea is to determinate the masks of the important edges both
for patients and controls and then merge them.
Borda counting
It has been used the Borda counting in order to do a ranking
of the edges (patients and controls)
After a cutting procedure has been applied on these graphs
A mask for controls
A mask for patients
Merge the two masks

8. Borda + strong/weak ties
Strong/weak ties cutting
Intuition
Identify the most important connections (strong ties)
Identify the weak connections which have few strong ties in
the neighborhood

9. Strong/weak ties cutting
Algorithm
Data: Full connected graph
Result: Cutted graph
Relevants = ∅;
Computes Minimun Spanning Tree MST;
for each edge e ∈ MST do
add e to Relevants;
end
for each edge e /∈ MST do
if the neighborhood of e has few edges ∈ Relevants then
add e to Relevants;
end
end
Algorithm 1: Strong/weak ties algorithm

10. T-test + Strong/weak ties
Alternately to Borda t-test (µ) has been used for selecting
important edges
After has been applied a Bonferroni correction
Edges have been taken if their p-values was < 0.05
Since relevant edges were too much (≈ 5000) a strong/weak
ties cutting has been applied

11. T-test + Strong ties
T-test (mu = 0)
After a Bonferroni correction has been applied (p-value <
0.05)
But here only edges belonging to minimum spanning tree have
been taken

12. Contents
Preprocessing
Borda + strong/weak ties
T-test + strong/weak ties
T-test + Strong ties
Propagation
Model
Example
Results
Community detection
Spectral clustering
Spectral clustering results
Infomap
Infomap results
Mutual information
Conclusions

13. Propagation model
Definition
Goal
To find out how information spreading itself on these networks
Idea
Vertices can be in an active state or not
Active vertices tend to apply a pression on neighbors in order
to try to activate them
If a not active node receives the right amount of pression it
becomes active

14. Propagation model
Details
A set of starting active nodes has been choosen (seeds)
A node u not active becomes active if:
random(0, 1) ≤
pression(u)
capacity(u)
random(0, 1): is a random number in range (0, 1)
capacity(u): weighted sum of edges incoming to u
pression(u): weighted sum of edges incoming to u and
outcoming from active nodes

15. Propagation model
Example

16. Propagation model results
T-test + Strong/weak ties
Mean
Standard deviation

17. Contents
Preprocessing
Borda + strong/weak ties
T-test + strong/weak ties
T-test + Strong ties
Propagation
Model
Example
Results
Community detection
Spectral clustering
Spectral clustering results
Infomap
Infomap results
Mutual information
Conclusions

18. Community detection on graphs (1)
A community is a subset of vertices such that vertices in the
same community are strongly connected each other and
weakly connected with other community
Clustering on graphs

19. Community detection on graphs (2)
In this work the following algorithms have been used:
Spectral clustering
Infomap community detection algorithm
They have been used to find pattern in graphs

20. Community detection on graphs (3)
The clustering has been applied on brain areas (graph
vertices) of each subject
This procedure has been applied on both patients and controls
After it has been calcuted co-occurrence matrix on both
controls and patients

21. Spectral clustering
Input: graph ajacency matrix and an integer digit k (number
of cluster)
Calculate the first k eigenvector v1, v2, . . . , vk of the matrix
Build the matrix V ⊆ Rn×n with eigenvector as column
The row of the matrix V are the new points zi ∈ Rk
Clustering of the points zi with k-means algorithm

22. Spectral clustering
Borda + strong/weak ties
Figure: Controls

23. Spectral clustering
Borda + strong/weak ties
Figure: Patients

24. Spectral clustering: community
Borda + strong/weak ties
Figure: Controls

25. Spectral clustering: community
Borda + strong/weak ties
Figure: Patients

26. Spectral clustering
T-Test + Strong ties
Figure: Controls

27. Spectral clustering
T-Test + Strong ties
Figure: Patients

28. Infomap algorithm
It is based on random walk
It considers the weights of the edges and their direction
The idea is to maximize the probability that a walker remains
in the community where it has been generated
Futhermore it is important also how much disconnected
communities are

29. Infomap
Borda + strong/weak ties
Figure: Controls

30. Infomap
Borda + strong/weak ties
Figure: Patients

31. Infomap: community
Borda + strong/weak ties
Figure: Controls

32. Infomap: community
Borda + strong/weak ties
Figure: Patients

33. Infomap
T-Test + strong/weak ties
Figure: Controls

34. Infomap
T-Test + strong/weak ties
Figure: Patients

35. Mutual information
Dataset/Algorithm Spectral clustering Infomap algorithm
Borda + strong/weak ties 0.8354332 0.8614745
T-test + strong/weak ties 0.7337158 0.8430798
T-test + strong ties 0.6066828 0.748526

36. Contents
Preprocessing
Borda + strong/weak ties
T-test + strong/weak ties
T-test + Strong ties
Propagation
Model
Example
Results
Community detection
Spectral clustering
Spectral clustering results
Infomap
Infomap results
Mutual information
Conclusions

37. Conclusions
Several esperiments have been applied to DTI brain networks
Relevant networks have been estracted
Information propagation results have to be improvered
Community detection has detected some stable community