Metrics: Soft dynamic-time-warping divergence for FDataGrid

docs/refs.bib

@@ -397,12 +397,34 @@ @inbook{wasserman_2006_nonparametric_nw
 }
 
 @inbook{wasserman_2006_nonparametric_llr,
-    author = {Larry Wasserman},
+	author = {Larry Wasserman},
     title = {All of Nonparametric Statistics},
     chapter   = {Nonparametric Regression},
     pages     = {77},
     publisher = {Springer-Verlag New York},
     year = {2006},
     isbn = {978-0-387-25145-5},
     doi = {10.1007/0-387-30623-4}
+}
+
+@pnproceedings{Cuturi_2017_sdtw,
+	title = {Soft-{DTW}: a Differentiable Loss Function for Time-Series},
+	author = {Marco Cuturi and Mathieu Blondel},
+	booktitle = {Proceedings of the 34th International Conference on Machine Learning},
+	pages = {894 -- 903},
+	year = {2017},
+	volume = {70},
+	series = {Proceedings of Machine Learning Research},
+	publisher = {PMLR},
+}
+
+@inproceedings{Blondel_2021_sdtw_div,
+	author = {Blondel, Mathieu and Mensch, Arthur and Vert, Jean-Philippe},
+	title = {Differentiable Divergences Between Time Series},
+	booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
+	pages = {3853 -- 3861},
+	year = {2021},
+	volume = {130},
+	series = {Proceedings of Machine Learning Research},
+	publisher = {PMLR},
 }

skfda/misc/_math.py

@@ -324,7 +324,8 @@ def inner_product(
         )
 
     return (
-        np.einsum('n...,m...->nm...', arg1, arg2).sum(axis=-1)
+        np.dot(arg1, arg2.T)
+        # np.einsum('n...,m...->nm...', arg1, arg2).sum(axis=-1)
         if _matrix else (arg1 * arg2).sum(axis=-1)
     )
 
@@ -679,3 +680,4 @@ def cosine_similarity_matrix(
     return _clip_cosine(
         inner_matrix / norm1[:, np.newaxis] / norm2[np.newaxis, :],
     )
+

skfda/misc/metrics/__init__.py

@@ -22,3 +22,5 @@
     TransformationMetric,
     pairwise_metric_optimization,
 )
+
+from ._sdtw_distances import sdtwDivergence, sdtw_divergence