  Motifs are the most repetitive/frequent patterns of a time-series. The
discovery of motifs is crucial for practitioners in order to understand and
interpret the phenomena occurring in sequential data. Currently, motifs are
searched among series sub-sequences, aiming at selecting the most frequently
occurring ones. Search-based methods, which try out series sub-sequence as
motif candidates, are currently believed to be the best methods in finding the
most frequent patterns.
  However, this paper proposes an entirely new perspective in finding motifs.
We demonstrate that searching is non-optimal since the domain of motifs is
restricted, and instead we propose a principled optimization approach able to
find optimal motifs. We treat the occurrence frequency as a function and
time-series motifs as its parameters, therefore we \textit{learn} the optimal
motifs that maximize the frequency function. In contrast to searching, our
method is able to discover the most repetitive patterns (hence optimal), even
in cases where they do not explicitly occur as sub-sequences. Experiments on
several real-life time-series datasets show that the motifs found by our method
are highly more frequent than the ones found through searching, for exactly the
same distance threshold.
