Acronym: DTD_CType: Whole SeriesYear: 2014Publication: DAMI

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$_C$.
Source Code: Derivative Transform Distance Code
Published Results:Recreated Results:

Recreated
Dataset:Result:
Adiac0.6675
ArrowHead0.8205
Beef0.5457
BeetleFly0.8110
BirdChicken0.8310
Car0.7100
CBF0.9612
ChlorineConcentration0.7029
CinCECGtorso0.8197
Coffee0.9754
Computers0.7223
CricketX0.7597
CricketY0.7422
CricketZ0.7709
DiatomSizeReduction0.9394
DistalPhalanxOutlineCorrect0.7529
DistalPhalanxOutlineAgeGroup0.7367
DistalPhalanxTW0.6192
Earthquakes0.7027
ECG2000.8254
ECG50000.9268
ECGFiveDays0.8564
ElectricDevices0.7866
FaceAll0.9428
FaceFour0.8026
FacesUCR0.8950
FiftyWords0.7494
Fish0.8987
FordA0.7498
FordB0.7204
GunPoint0.9627
Ham0.7260
HandOutlines0.8542
Haptics0.3850
Herring0.5323
InlineSkate0.5136
InsectWingbeatSound0.4612
ItalyPowerDemand0.9388
LargeKitchenAppliances0.7915
Lightning20.7997
Lightning70.7073
Mallat0.9468
Meat0.9777
MedicalImages0.7556
MiddlePhalanxOutlineCorrect0.7767
MiddlePhalanxOutlineAgeGroup0.5801
MiddlePhalanxTW0.5045
MoteStrain0.7968
NonInvasiveFatalECGThorax10.8373
NonInvasiveFatalECGThorax20.8818
OliveOil0.8697
OSULeaf0.8786
PhalangesOutlinesCorrect0.7708
Phoneme0.2554
Plane0.9976
ProximalPhalanxOutlineCorrect0.8140
ProximalPhalanxOutlineAgeGroup0.7674
ProximalPhalanxTW0.7317
RefrigerationDevices0.5954
ScreenType0.5606
ShapeletSim0.6644
ShapesAll0.8402
SmallKitchenAppliances0.6686
SonyAIBORobotSurface10.8008
SonyAIBORobotSurface20.8656
StarlightCurves0.9632
Strawberry0.9558
SwedishLeaf0.8958
Symbols0.9631
SyntheticControl0.9925
ToeSegmentation10.7290
ToeSegmentation20.8258
Trace0.9962
TwoLeadECG0.9581
TwoPatterns0.9996
UWaveGestureLibraryX0.7691
UWaveGestureLibraryY0.6938
UWaveGestureLibraryZ0.6897
UWaveGestureLibraryAll0.9312
Wafer0.9923
Wine0.8874
WordSynonyms0.7117
Worms0.6190
WormsTwoClass0.7030
Yoga0.8661

Algorithm: