Exact Discovery of Length-Range Motifs

Motif discovery is the problem of finding unknown patterns that appear frequently in real valued timeseries. Several approaches have been proposed to solve this problem with no a-priori knowledge of the timeseries or motif characteristics. MK algorithm is the de facto standard exact motif discovery algorithm but it can discover a single motif of a known length. In this paper, we argue that it is not trivial to extend this algorithm to handle multiple motifs of variable lengths when constraints of maximum overlap are to be satisfied which is the case in many real world applications. The paper proposes an extension of the MK algorithm called MK++ to handle these conditions. We compare this extensions with a recently proposed approximate solution and show that it is not only guaranteed to find the exact top pair-motifs but that it is also faster. The proposed algorithm is then applied to several real-world time series.