DTI brain networks analysis
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Transcript of DTI brain networks analysis
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