We have seen length-invariant motifs and how resampling is at the core of the solution.
This brings us to our first problem with the algorithms, i.e. if the resampling rates are close to 1, the algorithms produce the same results with a standard Matrix Profile motif search. This happens because of the inaccuracy that creeps in due to the resampling method. Since it is impossible to get the exact resampling this problem shall remain and the standard same length motifs would have a smaller Euclidean distance. We could mitigate this problem by introducing weights corresponding to each resampling rate. Secondly, the resampling algorithm used here can be improved upon as hinted earlier. We can locally model the time series and extract needed data points from the model. Another approach would be to use a statistical interpolation method.
The algorithms use ABjoins that require a fixed length parameter for subsequence length.
This issue can be addressed by using one of the umpteen variable length motif discovery algorithms as a wrapper.
CONCLUSION
Motif discovery has been a key component to many time series data mining tasks. Four ways to compute length invariant motifs were discussed; as opposed to variable length motif discovery that tries to find the best subsequence lengths to look for a motif. These four algorithms, Iterative STOMP, Appended STAMP, Pruned STOMP and Piecewise STAMP were compared for efficiency and completion. Their utility was demonstrated through bird song analysis, power consumption data and through analysis on insect behavior. Limitations and problems with the algorithms were presented. Using the algorithms in conjunction with Matrix Profile can lead to a more efficient extraction of motifs.
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