Best path through the matrix in dynamic time wrapping: interpreting and implementation I read several papers and blog to understand how dynamic time wrapping (DTW) can be used to compare two time series data. I understand how to generate matrix and also understand how to choose best path.
Now my question is what does this best path tells me or how can I tell these two time series are similar or not similar?
I understand how to implement DTW but could not understand how to interpret it.
 A: Assuming that the two signals $s_1$ and $s_2$ are of the same length, from a purely qualitative perspective the closest that this "best path" is to a diagonal the least amount of warping is required. More formally, as the DTW distance between $s_1$ and $s_2$ is the cost of transforming the entire series of $s_1$ into $s_2$ and the smaller this value is the higher the similarity of the signal of $s_1$ is to $s_2$. 
Tomašev et al. (2015) "Hubness-aware classification, instance selection and feature construction: Survey and extensions to time-series" has a nice a succinct presentation of DTW and how this can be used for feature construction encapsulating difference between two signals.
In addition to the standard view of DTW with Digital Signal Processing, DTW has draw attention within Statistics when it comes to Functional Data Analysis within the context of "registration" and the analysis of phase differences instead of only amplitude. Marron et al. (2015) "Functional Data Analysis of Amplitude and Phase Variation" give a full presentation of the subject, especially how the warping functions (the "best path" in the context of original DSP) can be used for further analysis.
