FIX clip small values in PLS cross-decomposition for increased stability (scikit-learn#13903)

Author: thomasjpfan

doc/whats_new/v0.20.rst

@@ -31,6 +31,13 @@ The bundled version of joblib was upgraded from 0.13.0 to 0.13.2.
   ``remainder`` transformer.
   :pr:`14237` by `Andreas Schuderer <schuderer>`.
 
+:mod:`sklearn.decomposition`
+............................
+
+- |Fix| Fixed a bug in :class:`cross_decomposition.CCA` improving numerical 
+  stability when `Y` is close to zero. :pr:`13903` by `Thomas Fan`_.
+
+
 :mod:`sklearn.model_selection`
 ..............................
 

sklearn/cross_decomposition/pls_.py

@@ -285,6 +285,7 @@ def fit(self, X, Y):
         self.n_iter_ = []
 
         # NIPALS algo: outer loop, over components
+        Y_eps = np.finfo(Yk.dtype).eps
         for k in range(self.n_components):
             if np.all(np.dot(Yk.T, Yk) < np.finfo(np.double).eps):
                 # Yk constant
@@ -293,6 +294,10 @@ def fit(self, X, Y):
             # 1) weights estimation (inner loop)
             # -----------------------------------
             if self.algorithm == "nipals":
+                # Replace columns that are all close to zero with zeros
+                Yk_mask = np.all(np.abs(Yk) < 10 * Y_eps, axis=0)
+                Yk[:, Yk_mask] = 0.0
+
                 x_weights, y_weights, n_iter_ = \
                     _nipals_twoblocks_inner_loop(
                         X=Xk, Y=Yk, mode=self.mode, max_iter=self.max_iter,