**Description: ** | Górecki and Łuczak proposed an extension of DD$_{DTW}$ that uses DTW in conjunction with transforms and derivatives. They propose and evaluate combining DD$_{DTW}$ with distances on date transformed with the sin, cosine and Hilbert transform. We implement the cosine version (see Algorithm 5), where function $cos$ transforms a series ${\bf a}$ into ${\bf c}$ using the formula
$$c_i = \sum_{j=1}^m a_j \cos \left( \frac{\Pi}{2} \left( j - \frac{1}{2} \right)(i-1) \right)\;\; i=1 \ldots m.$$ The two parameters $\alpha$ and $\beta$ are found through a grid search.
DD$_{DTW}$ was evaluated on single train test splits of 20 UCR datasets, CID$_{DTW}$ on 43 datasets and DTD$_C$ on 47. We can recreate results that are not significantly different to those published for all three algorithms. All papers claim superiority to DTW. The small sample size for DD$_{DTW}$ makes this claim debatable, but the published results for CID$_{DTW}$ and DTD$_C$ are both significantly better than DTW. On published results, DTD$_C$ is significantly more accurate than CID$_{DTW}$ and CID$_{DTW}$ is significantly better than DD$_{DTW}$. We can reproduce results not significantly different to those published for DD$_{DTW}$, CID$_{DTW}$ and DTD$_C$. |