  In this paper we present a novel algorithm and efficient data structure for
anomaly detection based on temporal data. Time-series data are represented by a
sequence of symbolic time intervals, describing increasing and decreasing
trends, in a compact way using gradient temporal abstraction technique. Then we
identify unusual subsequences in the resulting sequence using dynamic data
structure based on the geometric observations supporting polylogarithmic update
and query times. Moreover, we introduce a new parameter to control the pairwise
difference between the corresponding symbols in addition to a distance metric
between the subsequences. Experimental results on a public DNS network traffic
dataset show the superiority of our approach compared to the baselines.
