  Detecting repeated variable-length patterns, also called variable-length
motifs, has received a great amount of attention in recent years. Current
state-of-the-art algorithm utilizes fixed-length motif discovery algorithm as a
subroutine to enumerate variable-length motifs. As a result, it may take hours
or days to execute when enumeration range is large. In this work, we introduce
an approximate algorithm called HierarchIcal based Motif Enumeration (HIME) to
detect variable-length motifs with a large enumeration range in million-scale
time series. We show in the experiments that the scalability of the proposed
algorithm is significantly better than that of the state-of-the-art algorithm.
Moreover, the motif length range detected by HIME is considerably larger than
previous sequence-matching based approximate variable-length motif discovery
approach. We demonstrate that HIME can efficiently detect meaningful
variable-length motifs in long, real world time series.
