Acronym: MSMType: Whole SeriesYear: 2013Publication: 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
Published Results:Recreated Results:

Published
Dataset:Result:
Adiac0.384
Beef0.5
CBF0.012
Coffee0.236
FaceAll0.189
FaceFour0.057
FiftyWords0.196
Fish0.08
GunPoint0.06
Lightning20.164
Lightning70.233
OliveOil0.167
OSULeaf0.198
SwedishLeaf0.104
SyntheticControl0.027
Trace0.07
TwoPatterns0.001
Wafer0.004
Yoga0.143

This algorithm doesn't have any recreated results.

Algorithm: