Acronym: MSM Type: Whole Series Year: 2013 Publication: TKDE

 Description: Stefan $et\:al.$ present MSM distance, a metric that is conceptually similar to other edit distance-based approaches, where similarity is calculated by using a set of operations to transform a given series into a target series. Move is synonymous with a substitute operation, where one value is replaced by another. The split operation inserts an identical copy of a value immediately after itself, and the merge operation is used to delete a value if it directly follows an identical value. $$C(a_i,a_{i-1},b_j) = \left\{ \begin{array}{l} \mbox{c if a_{i-1} \leq a_i \leq b_j  or a_{i-1} \geq a_i \geq b_j} \\ \mbox{c+min(|a_i-a_{i-1}|,|a_i-b_j|) otherwise.} \end{array} \right.$$ We have implemented WDTW, TWE, MSM and other commonly used time domain distance measures (such as LCSS and ERP). They are available in the package elastic_distance_measures. We have generated results that are not significantly different to those published when using these distances with 1-NN. In it was shown that there is no significant difference between 1-NN with DTW and with WDTW, TWE or MSM on a set of 72 problems using a single train/test split. In Section 4 we revisit this result with more data and resamples rather than a train/test split. There are a group of algorithms that are based on whole series similarity of the first order differences of the series, $$a'_i = a_i-a_{i+1} \;\; i=1 \ldots m-1,$$ which we refer to as diff. Various methods that have used just the differences have been described, but the most successful approaches combine distance in the time domain and the difference domain. Source Code: Move-Split-Merge Code
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 Published Dataset: Result: Adiac 0.384 Beef 0.5 CBF 0.012 Coffee 0.236 FaceAll 0.189 FaceFour 0.057 FiftyWords 0.196 Fish 0.08 GunPoint 0.06 Lightning2 0.164 Lightning7 0.233 OliveOil 0.167 OSULeaf 0.198 SwedishLeaf 0.104 SyntheticControl 0.027 Trace 0.07 TwoPatterns 0.001 Wafer 0.004 Yoga 0.143

 This algorithm doesn't have any recreated results.

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