Visualising the structural and functional connectivity of a neural network.

mat_reorder.py

##Visualising the structural and functional connectivity
##of a neural network.
##by Alexandros Kourkoulas-Chondrorizos
##v0.1
##This is a simple function that calculates the covariance
##matrix of a neural network based on its activity. It then
##reorders the covariance matrix to obtain a depiction of
##functional connectivity and based on that reordering also
##rearranges the connectivity matrix in order to obtain a
##clearer picture of its structural connectivity. Put simply,
##it brings closer neurons that are structurally and 
##functionally connected. All it needs is the network's
##connectivity matrix and a sample of its activity in order to
##calculate the covariance matrix. S should be a N-by-N matrix
##where N is the number of neurons in the neural network and
##Nact should be a N-by-T matrix where N is the same as above
##and T is the length of the simulation.

def mat_reorder(S,Nact):
    #compute covariance matrix
    Cm=cov(Nact)
    #compute dendrogram
    Y=sch.linkage(D,method='centroid')
    Z=sch.dendrogram(Y,orientation='right')
    index=Z['leaves']
    #reorder matrices
    Cm=Cm[index,:]
    Cm=Cm[:,index]
    S=S[index,:]
    S=S[:,index]

    #save reordered covariance and connectivity matrices
    figure(1),matshow(S,origin='lower'),xticks([]),yticks([]),
    title('Reordered Connectivity Matrix'),savefig('structural_connectivity.png')
    figure(2),matshow(Cm,origin='lower'),xticks([]),yticks([]),
    title('Reordered Covariance Matrix'),savefig('functional_connectivity.png')