# Theory of Dynamic Time Warping(DTW) in dtwclust package of the software R

I used to utilize dtwclust for my study and I got a problem. I have read a few studies and I understand the DTW distance like below picture.

source: A. Akl, S. Valaee, "Accelerometer-based gesture recognition via dynamic-time warping, affinity propagation, & compressive sensing," IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), pp.2270-2273, 2010.

and I read then "Comparing Time-Series Clustering Algorithms in R Using the dtwclust Package". The notation for DTW is different.

source: Alexis Sard´a-Espinosa, Comparing Time-Series Clustering Algorithms in R Using the dtwclust Package, pp.5-6

I don't understand what m_∅ is. They say it is a per-step weighting coefficient. anybody help me?? just give me clue. Thanks in advance.

That is a phi $\phi$, not a diameter ∅.
The small $m_\phi$ are weight terms, $M_\phi = \sum_i m_\phi$ is the normalization term to make them sum to 1.