DTI brain networks analysisSignificativity, propagation and community detection

Emanuele Pesce, Alessandro Merola

Neural Network and Knowledge DiscoveryUniversità degli studi di Salerno

July 2015

PreprocessingBorda + strong/weak tiesT-test + strong/weak tiesT-test + Strong ties

PropagationModelExampleResults

Community detectionSpectral clusteringSpectral clustering resultsInfomapInfomap resultsMutual information

Conclusions

ContentsPreprocessing

Borda + strong/weak tiesT-test + strong/weak tiesT-test + Strong ties

PropagationModelExampleResults

Community detectionSpectral clusteringSpectral clustering resultsInfomapInfomap resultsMutual information

Conclusions

Input Dataset

I 70 subjectsI 20 controlsI 50 patients (SLA)

I DTI dataI 90 regions of interest (ROI)

GraphsI Modelling the problem with graphsI Each graph has 90 vretices and 8100 edges (full connected)I The weight of an edge stands for the number of streamline

between two brain areas

Choosing significant edges

There is the need of ”pruning” the edges, removing those lesssignificant and keeping the most important ones

Three ways:I Borda + strong/weak tiesI T-test + strong/weak tiesI T-test + strong ties

Borda + strong/weak tiesBorda counting

The idea is to determinate the masks of the important edges bothfor patients and controls and then merge them.

Borda countingI It has been used the Borda counting in order to do a ranking

of the edges (patients and controls)I After a cutting procedure has been applied on these graphs

I A mask for controlsI A mask for patients

I Merge the two masks

Borda + strong/weak tiesStrong/weak ties cutting

IntuitionI Identify the most important connections (strong ties)I Identify the weak connections which have few strong ties in

the neighborhood

Strong/weak ties cuttingAlgorithm

Data: Full connected graphResult: Cutted graphRelevants = ∅;Computes Minimun Spanning Tree MST;for each edge e ∈ MST do

add e to Relevants;endfor each edge e /∈ MST do

if the neighborhood of e has few edges ∈ Relevants thenadd e to Relevants;

endend

Algorithm 1: Strong/weak ties algorithm

T-test + Strong/weak ties

I Alternately to Borda t-test (µ) has been used for selectingimportant edges

I After has been applied a Bonferroni correctionI Edges have been taken if their p-values was < 0.05I Since relevant edges were too much (≈ 5000) a strong/weak

ties cutting has been applied

T-test + Strong ties

I T-test (mu = 0)I After a Bonferroni correction has been applied (p-value <

0.05)I But here only edges belonging to minimum spanning tree have

been taken

ContentsPreprocessing

Borda + strong/weak tiesT-test + strong/weak tiesT-test + Strong ties

PropagationModelExampleResults

Community detectionSpectral clusteringSpectral clustering resultsInfomapInfomap resultsMutual information

Conclusions

Propagation modelDefinition

GoalTo find out how information spreading itself on these networks

IdeaI Vertices can be in an active state or notI Active vertices tend to apply a pression on neighbors in order

to try to activate themI If a not active node receives the right amount of pression it

becomes active

Propagation modelDetails

I A set of starting active nodes has been choosen (seeds)I A node u not active becomes active if:

random(0, 1) ≤ pression(u)capacity(u)

I random(0, 1): is a random number in range (0, 1)I capacity(u): weighted sum of edges incoming to uI pression(u): weighted sum of edges incoming to u and

outcoming from active nodes

Propagation modelExample

Propagation model resultsT-test + Strong/weak ties

Mean Standard deviation

ContentsPreprocessing

Borda + strong/weak tiesT-test + strong/weak tiesT-test + Strong ties

PropagationModelExampleResults

Community detectionSpectral clusteringSpectral clustering resultsInfomapInfomap resultsMutual information

Conclusions

Community detection on graphs (1)I A community is a subset of vertices such that vertices in the

same community are strongly connected each other andweakly connected with other community

I Clustering on graphs

Community detection on graphs (2)

I In this work the following algorithms have been used:I Spectral clusteringI Infomap community detection algorithm

I They have been used to find pattern in graphs

Community detection on graphs (3)

I The clustering has been applied on brain areas (graphvertices) of each subject

I This procedure has been applied on both patients and controlsI After it has been calcuted co-occurrence matrix on both

controls and patients

Spectral clustering

I Input: graph ajacency matrix and an integer digit k (numberof cluster)

I Calculate the first k eigenvector v1, v2, . . . , vk of the matrixI Build the matrix V ⊆ Rn×n with eigenvector as columnI The row of the matrix V are the new points zi ∈ Rk

I Clustering of the points zi with k-means algorithm

Spectral clusteringBorda + strong/weak ties

Figure: Controls

Spectral clusteringBorda + strong/weak ties

Figure: Patients

Spectral clustering: communityBorda + strong/weak ties

Figure: Controls

Spectral clustering: communityBorda + strong/weak ties

Figure: Patients

Spectral clusteringT-Test + Strong ties

Figure: Controls

Spectral clusteringT-Test + Strong ties

Figure: Patients

Infomap algorithm

I It is based on random walkI It considers the weights of the edges and their directionI The idea is to maximize the probability that a walker remains

in the community where it has been generatedI Futhermore it is important also how much disconnected

communities are

InfomapBorda + strong/weak ties

Figure: Controls

InfomapBorda + strong/weak ties

Figure: Patients

Infomap: communityBorda + strong/weak ties

Figure: Controls

Infomap: communityBorda + strong/weak ties

Figure: Patients

InfomapT-Test + strong/weak ties

Figure: Controls

InfomapT-Test + strong/weak ties

Figure: Patients

Mutual information

Dataset/Algorithm Spectral clustering Infomap algorithmBorda + strong/weak ties 0.8354332 0.8614745T-test + strong/weak ties 0.7337158 0.8430798T-test + strong ties 0.6066828 0.748526

ContentsPreprocessing

Borda + strong/weak tiesT-test + strong/weak tiesT-test + Strong ties

PropagationModelExampleResults

Community detectionSpectral clusteringSpectral clustering resultsInfomapInfomap resultsMutual information

Conclusions

Conclusions

I Several esperiments have been applied to DTI brain networksI Relevant networks have been estractedI Information propagation results have to be improveredI Community detection has detected some stable community