Spectral Perturbation of Small-World Networks with Application to Brain Disease Detection

In this project, I am trying to apply this model to classify networks generated from human brain. Since small-world networks are essentially random graphs whose adjacency matrices are random matrices, I first study the spectrum of them. Next, I assume that a sampled brain network is perturbed version of an averaged network: either that over people with Alzheimer’s disease, or over healthy people. In order to diagnose a new patient, I calculate the spectral correlation (i.e., correlation of eigenvalue distributions) between the network of this patient and sampled networks in a database, where we know each data point is generated from whether a sick or healthy person. These correlations are then used to determine the status of the patient, which is effective when ówe only have a relative small database compared against the dimension of each network. Apart from this, I also briefly mention an extension of the small-world network model to fit the observed brain networks.