PHD Defense: Ruituo Fan
Clustering and change point detection in time series with community structure
Clustering is a central problem in unsupervised learning. We study the problem of clustering based on a collection of random processes driven by certain latent community structure in networks. We show that global optimum of K-means can recover the groups exactly with high probability given enough observations across time. We will also consider vector autoregressive model driven by stochastic block model as a special case, but with change points. We show that the model can be studied under the structural break framework when the community structure is fixed and known. Performance of algorithms for both community detection and change point detection is compared in numerical experiments.