ENH: correlation function accepts method being a callable

doc/source/computation.rst

@@ -153,6 +153,21 @@ Like ``cov``, ``corr`` also supports the optional ``min_periods`` keyword:
    frame.corr(min_periods=12)
 
 
+.. versionadded:: 0.24.0
+
+The ``method`` argument can also be a callable for a generic correlation
+calculation. In this case, it should be a single function
+that produces a single value from two ndarray inputs. Suppose we wanted to
+compute the correlation based on histogram intersection:
+
+.. ipython:: python
+
+   # histogram intersection
+   histogram_intersection = lambda a, b: np.minimum(
+       np.true_divide(a, a.sum()), np.true_divide(b, b.sum())
+   ).sum()
+   frame.corr(method=histogram_intersection)
+
 A related method :meth:`~DataFrame.corrwith` is implemented on DataFrame to 
 compute the correlation between like-labeled Series contained in different 
 DataFrame objects.

doc/source/whatsnew/v0.24.0.txt

@@ -20,6 +20,8 @@ New features
 - :func:`DataFrame.to_parquet` now accepts ``index`` as an argument, allowing
 the user to override the engine's default behavior to include or omit the
 dataframe's indexes from the resulting Parquet file. (:issue:`20768`)
+- :meth:`DataFrame.corr` and :meth:`Series.corr` now accept a callable for generic calculation methods of correlation, e.g. histogram intersection (:issue:`22684`)
+
 
 .. _whatsnew_0240.enhancements.extension_array_operators:
 

pandas/core/frame.py

@@ -6672,10 +6672,14 @@ def corr(self, method='pearson', min_periods=1):
 
         Parameters
         ----------
-        method : {'pearson', 'kendall', 'spearman'}
+        method : {'pearson', 'kendall', 'spearman'} or callable
             * pearson : standard correlation coefficient
             * kendall : Kendall Tau correlation coefficient
             * spearman : Spearman rank correlation
+            * callable: callable with input two 1d ndarrays
+                and returning a float
+                .. versionadded:: 0.24.0
+
         min_periods : int, optional
             Minimum number of observations required per pair of columns
             to have a valid result. Currently only available for pearson
@@ -6684,6 +6688,18 @@ def corr(self, method='pearson', min_periods=1):
         Returns
         -------
         y : DataFrame
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> histogram_intersection = lambda a, b: np.minimum(a, b
+        ... ).sum().round(decimals=1)
+        >>> df = pd.DataFrame([(.2, .3), (.0, .6), (.6, .0), (.2, .1)],
+        ...                   columns=['dogs', 'cats'])
+        >>> df.corr(method=histogram_intersection)
+              dogs cats
+        dogs   1.0  0.3
+        cats   0.3  1.0
         """
         numeric_df = self._get_numeric_data()
         cols = numeric_df.columns
@@ -6695,7 +6711,7 @@ def corr(self, method='pearson', min_periods=1):
         elif method == 'spearman':
             correl = libalgos.nancorr_spearman(ensure_float64(mat),
                                                minp=min_periods)
-        elif method == 'kendall':
+        elif method == 'kendall' or callable(method):
             if min_periods is None:
                 min_periods = 1
             mat = ensure_float64(mat).T

pandas/core/nanops.py

@@ -766,6 +766,8 @@ def nancorr(a, b, method='pearson', min_periods=None):
 def get_corr_func(method):
     if method in ['kendall', 'spearman']:
         from scipy.stats import kendalltau, spearmanr
+    elif callable(method):
+        return method
 
     def _pearson(a, b):
         return np.corrcoef(a, b)[0, 1]

pandas/core/series.py

@@ -1910,23 +1910,37 @@ def corr(self, other, method='pearson', min_periods=None):
         Parameters
         ----------
         other : Series
-        method : {'pearson', 'kendall', 'spearman'}
+        method : {'pearson', 'kendall', 'spearman'} or callable
             * pearson : standard correlation coefficient
             * kendall : Kendall Tau correlation coefficient
             * spearman : Spearman rank correlation
+            * callable: callable with input two 1d ndarray
+                and returning a float
+                .. versionadded:: 0.24.0
+
         min_periods : int, optional
             Minimum number of observations needed to have a valid result
 
 
         Returns
         -------
         correlation : float
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> histogram_intersection = lambda a, b: np.minimum(a, b
+        ... ).sum().round(decimals=1)
+        >>> s1 = pd.Series([.2, .0, .6, .2])
+        >>> s2 = pd.Series([.3, .6, .0, .1])
+        >>> s1.corr(s2, method=histogram_intersection)
+        0.3
         """
         this, other = self.align(other, join='inner', copy=False)
         if len(this) == 0:
             return np.nan
 
-        if method in ['pearson', 'spearman', 'kendall']:
+        if method in ['pearson', 'spearman', 'kendall'] or callable(method):
             return nanops.nancorr(this.values, other.values, method=method,
                                   min_periods=min_periods)
 

pandas/tests/series/test_analytics.py

@@ -789,6 +789,38 @@ def test_corr_invalid_method(self):
         with tm.assert_raises_regex(ValueError, msg):
             s1.corr(s2, method="____")
 
+    def test_corr_callable_method(self):
+        # simple correlation example
+        # returns 1 if exact equality, 0 otherwise
+        my_corr = lambda a, b: 1. if (a == b).all() else 0.
+
+        # simple example
+        s1 = Series([1, 2, 3, 4, 5])
+        s2 = Series([5, 4, 3, 2, 1])
+        expected = 0
+        tm.assert_almost_equal(
+            s1.corr(s2, method=my_corr),
+            expected)
+
+        # full overlap
+        tm.assert_almost_equal(
+            self.ts.corr(self.ts, method=my_corr), 1.)
+
+        # partial overlap
+        tm.assert_almost_equal(
+            self.ts[:15].corr(self.ts[5:], method=my_corr), 1.)
+
+        # No overlap
+        assert np.isnan(
+            self.ts[::2].corr(self.ts[1::2], method=my_corr))
+
+        # dataframe example
+        df = pd.DataFrame([s1, s2])
+        expected = pd.DataFrame([
+            {0: 1., 1: 0}, {0: 0, 1: 1.}])
+        tm.assert_almost_equal(
+            df.transpose().corr(method=my_corr), expected)
+
     def test_cov(self):
         # full overlap
         tm.assert_almost_equal(self.ts.cov(self.ts), self.ts.std() ** 2)