  Most real-world networks exhibit community structure, a phenomenon
characterized by existence of node clusters whose intra-edge connectivity is
stronger than edge connectivities between nodes belonging to different
clusters. In addition to facilitating a better understanding of network
behavior, community detection finds many practical applications in diverse
settings. Communities in online social networks are indicative of shared
functional roles, or affiliation to a common socio-economic status, the
knowledge of which is vital for targeted advertisement. In buyer-seller
networks, community detection facilitates better product recommendations.
Unfortunately, reliability of community assignments is hindered by anomalous
user behavior often observed as unfair self-promotion, or "fake"
highly-connected accounts created to promote fraud. The present paper advocates
a novel approach for jointly tracking communities while detecting such
anomalous nodes in time-varying networks. By postulating edge creation as the
result of mutual community participation by node pairs, a dynamic factor model
with anomalous memberships captured through a sparse outlier matrix is put
forth. Efficient tracking algorithms suitable for both online and decentralized
operation are developed. Experiments conducted on both synthetic and real
network time series successfully unveil underlying communities and anomalous
nodes.
