rmse -> distance correlation (#811)

* rmse -> distance correlation

* import stats

Former-commit-id: 8dd58b6

Author: scottgigante-immunai

openproblems/tasks/dimensionality_reduction/README.md

@@ -23,12 +23,12 @@ data for visualization and interpretation.
 
 ## The metrics
 
-* **Root mean square error**: the square root of the mean squared difference between
+* **Distance correlation**: the Spearman correlation between
   ground truth distances in the high-dimensional data and Euclidean distances in the
-  dimension-reduced data, invariant to scalar multiplication. *RMSE* computes
-  high-dimensional distances in Euclidean space, while *RMSE (spectral)* computes
-  [diffusion distances](http://dx.doi.org/10.1016/j.acha.2006.04.006) (i.e. Euclidean
-  distances on the [Laplacian Eigenmap](http://dx.doi.org/10.1162/089976603321780317)).
+  dimension-reduced data, invariant to scalar multiplication. *Distance correlation*
+  computes high-dimensional distances in Euclidean space, while *Distance correlation
+  (spectral)* computes [diffusion distances](http://dx.doi.org/10.1016/j.acha.2006.04.006)
+  (i.e. Euclidean distances on the [Laplacian Eigenmap](http://dx.doi.org/10.1162/089976603321780317)).
 * **Trustworthiness**: a measurement of similarity between the rank of each point's
   nearest neighbors in the high-dimensional data and the reduced data ([Venna & Kaski,
   2001](https://openproblems.bio/bibliography#venna2001neighborhood)).

openproblems/tasks/dimensionality_reduction/metrics/__init__.py

@@ -1,10 +1,10 @@
 from .density import density_preservation
+from .distance_correlation import distance_correlation
+from .distance_correlation import distance_correlation_spectral
 from .nn_ranking import continuity
 from .nn_ranking import lcmc
 from .nn_ranking import qglobal
 from .nn_ranking import qlocal
 from .nn_ranking import qnn
 from .nn_ranking import qnn_auc
-from .root_mean_square_error import rmse
-from .root_mean_square_error import rmse_spectral
 from .trustworthiness import trustworthiness

…uction/metrics/root_mean_square_error.py …eduction/metrics/distance_correlation.pyopenproblems/tasks/dimensionality_reduction/metrics/root_mean_square_error.py renamed to openproblems/tasks/dimensionality_reduction/metrics/distance_correlation.py openproblems/tasks/dimensionality_reduction/metrics/root_mean_square_error.py renamed to openproblems/tasks/dimensionality_reduction/metrics/distance_correlation.py

@@ -2,24 +2,23 @@
 from ....tools.normalize import log_cpm
 
 
-def _rmse(X, X_emb):
-    import scipy.optimize
+def _distance_correlation(X, X_emb):
     import scipy.spatial
+    import scipy.stats
 
     high_dimensional_distance_vector = scipy.spatial.distance.pdist(X)
     low_dimensional_distance_vector = scipy.spatial.distance.pdist(X_emb)
-    _, rmse = scipy.optimize.nnls(
-        low_dimensional_distance_vector[:, None], high_dimensional_distance_vector
-    )
-    return rmse
+    return scipy.stats.spearmanr(
+        low_dimensional_distance_vector, high_dimensional_distance_vector
+    )[0]
 
 
 @metric(
-    metric_name="RMSE",
-    maximize=False,
-    paper_reference="kruskal1964mds",
+    metric_name="Distance correlation",
+    maximize=True,
+    paper_reference="schober2018correlation",
 )
-def rmse(adata, n_svd=200):
+def distance_correlation(adata, n_svd=200):
     """Calculate the root mean squared error.
 
     Computes (RMSE) between the full (or processed) data matrix and the
@@ -30,15 +29,15 @@ def rmse(adata, n_svd=200):
     adata = log_cpm(adata)
 
     X = sklearn.decomposition.TruncatedSVD(n_svd).fit_transform(adata.X)
-    return _rmse(X, adata.obsm["X_emb"])
+    return _distance_correlation(X, adata.obsm["X_emb"])
 
 
 @metric(
-    metric_name="RMSE (spectral)",
-    maximize=False,
+    metric_name="Distance correlation (spectral)",
+    maximize=True,
     paper_reference="coifman2006diffusion",
 )
-def rmse_spectral(adata, n_comps=200):
+def distance_correlation_spectral(adata, n_comps=200):
     """Calculate the spectral root mean squared error
 
     Computes (RMSE) between high-dimensional Laplacian eigenmaps on the full (or
@@ -57,4 +56,4 @@ def rmse_spectral(adata, n_comps=200):
     X = umap.spectral.spectral_layout(
         adata.X, graph, n_comps, random_state=np.random.default_rng()
     )
-    return _rmse(X, adata.obsm["X_emb"])
+    return _distance_correlation(X, adata.obsm["X_emb"])