  Network size is a fundamental statistic for a peer-to-peer system but is
generally considered to contain too little information to be useful. However,
most existing work only considers the metric by itself and does not explore
what features could be extracted from this seem- ingly trivial metric. In this
paper, we show that Fourier transform allows us to extract frequency features
from such time series data, which can further be used to characterize user
behaviors and detect system anoma- lies in a peer-to-peer system automatically
without needing to resort to visual comparisons. By using the proposed
algorithm, our system suc- cessfully discovers and clusters countries of
similar user behavior and captures the anomalies like Sybil attacks and other
real-world events with high accuracy. Our work in this paper highlights the
usefulness of more advanced time series processing techniques in analyzing
network measurements.
