**Description: ** | Jeong $et\:al.$ describe WDTW, which adds a multiplicative weight penalty based on the warping distance between points in the warping path. It favours reduced warping, and is a smooth alternative to the cutoff point approach of using a warping window. When creating the distance matrix $M$, a weight penalty $w_{|i-j|}$ for a warping distance of $|i-j|$ is applied, so that
$$M_{i,j}= w_{|i-j|} (a_i-b_j)^2.$$
A logistic weight function is used, so that a warping of $a$ places imposes a weighting of
$$w(a)=\frac{w_{max}}{1+e^{-g\cdot(a-m/2)}},$$
where $w_{max}$ is an upper bound on the weight (set to 1), $m$ is the series length and $g$ is a parameter that controls the penalty level for large warpings. The larger $g$ is, the greater the penalty for warping. |