Metrics: Soft dynamic-time-warping divergence for FDataGrid

docs/refs.bib

@@ -63,6 +63,17 @@ @article{berrendero+cuevas+torrecilla_2018_hilbert
     URL = {https://doi.org/10.1080/01621459.2017.1320287}
 }
 
+@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},
+}
+
 @inproceedings{breunig++_2000_outliers,
     author = {Breunig, Markus and Kriegel, Hans-Peter and Ng, Raymond and Sander, Joerg},
     year = {2000},
@@ -111,6 +122,17 @@ @article{cuevas++_2004_anova
     doi = {10.1016/j.csda.2003.10.021}
 }
 
+@inproceedings{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},
+}
+
 @article{dai+genton_2018_visualization,
     author = {Wenlin Dai and Marc G. Genton},
     title = {Multivariate Functional Data Visualization and Outlier Detection},

skfda/misc/_math.py

@@ -327,7 +327,8 @@ def inner_product(
         )
     elif isinstance(arg1, np.ndarray) and isinstance(arg2, np.ndarray):
         return (  # type: ignore[no-any-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)
         )
 
@@ -675,3 +676,4 @@ def cosine_similarity_matrix(
     return _clip_cosine(
         inner_matrix / norm1[:, np.newaxis] / norm2[np.newaxis, :],
     )
+

skfda/misc/metrics/__init__.py

@@ -30,6 +30,7 @@
         ],
         "_mahalanobis": ["MahalanobisDistance"],
         "_parse": ["PRECOMPUTED"],
+        "_sdtw_distances": ["sdtwDivergence"],
         "_utils": [
             "NormInducedMetric",
             "PairwiseMetric",
@@ -63,6 +64,7 @@
     )
     from ._mahalanobis import MahalanobisDistance as MahalanobisDistance
     from ._parse import PRECOMPUTED as PRECOMPUTED
+    from ._sdtw_distances import sdtwDivergence
     from ._utils import (
         NormInducedMetric as NormInducedMetric,
         PairwiseMetric as PairwiseMetric,