**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. |