Implement Metric methods and tests

cfs/Selection.py

@@ -1,3 +1,86 @@
+from math import log
+import numpy as np
+
+
+class Metrics:
+    @staticmethod
+    def conditional_entropy(x, y, base=2):
+        """quantifies the amount of information needed to describe the outcome
+        of Y given that the value of X is known
+        computes H(Y|X)
+
+        Parameters
+        ----------
+        x : np.array
+            values of the variable
+        y : np.array
+            array of labels
+        base : int, optional
+            base of the logarithm, by default 2
+
+        Returns
+        -------
+        float
+            conditional entropy of y given x
+        """
+        xy = np.c_[x, y]
+        return Metrics.entropy(xy, base) - Metrics.entropy(x, base)
+
+    @staticmethod
+    def entropy(y, base=2):
+        """measure of the uncertainty in predicting the value of y
+
+        Parameters
+        ----------
+        y : np.array
+            array of labels
+        base : int, optional
+            base of the logarithm, by default 2
+
+        Returns
+        -------
+        float
+            entropy of y
+        """
+        _, count = np.unique(y, return_counts=True, axis=0)
+        proba = count.astype(float) / len(y)
+        proba = proba[proba > 0.0]
+        return np.sum(proba * np.log(1.0 / proba)) / log(base)
+
+    @staticmethod
+    def information_gain(x, y, base=2):
+        """Measures the reduction in uncertainty about the value of y when the
+        value of X is known (also called mutual information)
+        (https://www.sciencedirect.com/science/article/pii/S0020025519303603)
+
+        Parameters
+        ----------
+        x : np.array
+            values of the variable
+        y : np.array
+            array of labels
+        base : int, optional
+            base of the logarithm, by default 2
+
+        Returns
+        -------
+        float
+            Information gained
+        """
+        return Metrics.entropy(y, base) - Metrics.conditional_entropy(
+            x, y, base
+        )
+
+    @staticmethod
+    def symmetrical_uncertainty(x, y):
+
+        return (
+            2.0
+            * Metrics.information_gain(x, y)
+            / (Metrics.entropy(x) + Metrics.entropy(y))
+        )
+
+
 class CFS:
     def __init__(self, a):
         self.a = a