Distance metrics

Wildboar support both subsequence distance using distance.pairwise_subsequence_distance() and traditional distances using distance.pairwise_distance(). These and related functions support different metrics, as specified by the metric argument and metric parameters using the metric_params argument.

Subsequence distance metrics

Metric name	metric	metric_params	Comments
Euclidean	"euclidean"	{}
Normalized Euclidean	"normalized_euclidean"	{}	Euclidean distance, where length has been scaled to have unit norm. Undefined cases result in 0.
Scaled Euclidean	"scaled_euclidean" or "mass"	{}	Scales each subsequence to have zero mean and unit variance.
Manhattan	"manhattan"	{}
Minkowski	"minkowski"	{}
Chebyshev	"chebyshev"	{}
Cosine	"cosine"	{}
Angular	"angular"	{}
Dynamic time warping	"dtw"	{"r": float}	Window r in [0, 1]
Scaled DTW	"scaled_dtw"	{"r": float}	Window r in [0, 1]

Distance metrics

Metric name	metric	metric_params	Comments
Euclidean	"euclidean"	{}
Normalized Euclidean	"normalized_euclidean"	{}	Euclidean distance, where length has been scaled to have unit norm. Undefined cases result in 0.
Manhattan	"manhattan"	{}
Minkowski	"minkowski"	{}
Chebyshev	"chebyshev"	{}
Cosine	"cosine"	{}
Angular	"angular"	{}
Longest common subsequence [1]	"lcss"	{r: float, threshold: float}	Window r in [0, 1]. Match threshold, default 1. Elastic.
Edit distance with real penalty [2]	"erp"	{r: float, g: float}	Window r in [0, 1]. Gap penalty g, default 0. Elastic.
Edit distance for real sequences [3]	"edr"	{r: float, threshold: float}	Window r in [0, 1]. Match threshold, default 1/4*max(std(x), std(y)). Elastic.
Move-split-merge [4]	"msm"	{r: float, c: float}	Window r in [0, 1]. Split/merge cost c, default 1. Elastic.
Time Warp Edit distance [5]	"twe"	{r: float, edit_penalty: float, stiffness: float}	Window r in [0, 1]. Edit penalty (\(\lambda\)), default 1. Stiffness (\(\nu\)), default 0.001.
Dynamic time warping	"dtw"	{"r": float}	Window r in [0, 1]. Elastic.
Weighted DTW	"wdtw"	{"r": float, "g": float}	Window r in [0, 1]. Phase difference penalty g. Elastic.
Derivative DTW	"ddtw"	{"r": float}	Window r in [0, 1]. Elastic.
Weighted Derivative DTW	"wddtw"	{"r": float, "g": float}	Window r in [0, 1]. Phase difference penalty g. Elastic.

References

[1] Hirschberg, D. (1977).

Algorithms for the longest common subsequence problem. Journal of the ACM (JACM).

[2] Chen, L., & Ng, R. (2004).

On the Marriage of Lp-Norms and Edit Distance (30). Proceedings of the Thirtieth International Conference on Very Large Data Base.

[3] Chen, L., Özsu, M. T., & Oria, V. (2005).

Robust and fast similarity search for moving object trajectories. Proceedings from Proceedings of the International Conference on Management of Data

[4] Stefan, A., Athitsos, V., & Das, G. (2013).

The Move-Split-Merge Metric for Time Series. IEEE Transactions on Knowledge and Data Engineering, 25(6), 1425-1438.

[5] Marteau, P.-F. (2008).

Time warp edit distance with stiffness adjustment for time series matching. IEEE transactions on pattern analysis and machine intelligence, 31(2), 306-318.