Create pearson_correlation.py

Author: LuisOfL

machine_learning/pearson_correlation.py

@@ -0,0 +1,53 @@
+import numpy as np
+
+
+def pearson_correlation(x: np.ndarray, y: np.ndarray) -> float:
+    """
+    Calculate the Pearson correlation coefficient (PCC) between two arrays.
+
+    Pearson correlation measures the linear relationship between two datasets,
+    returning a value between -1 and 1:
+      - 1   indicates a perfect positive linear correlation
+      - 0   indicates no linear correlation
+      - -1  indicates a perfect negative linear correlation
+
+    Formula:
+    r = Σ((x - mean(x)) * (y - mean(y))) / sqrt(Σ(x - mean(x))^2 * Σ(y - mean(y))^2)
+
+    Reference: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+
+    Parameters:
+    - x: 1D numpy array of values
+    - y: 1D numpy array of values
+
+    Returns:
+    - The Pearson correlation coefficient (float)
+
+      a = np.array([1, 2, 3, 4, 5])
+      b = np.array([2, 4, 6, 8, 10])
+      float(np.round(pearson_correlation(a, b), 5))
+    1.0
+      a = np.array([1, 2, 3, 4, 5])
+      b = np.array([10, 9, 2, 6, 4])
+      float(np.round(pearson_correlation(a, b), 5))
+    -0.18845
+      a = np.array([1, 2, 3])
+      b = np.array([1, 2])
+      pearson_correlation(a, b)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input arrays must have the same length.
+    """
+    if len(x) != len(y):
+        raise ValueError("Input arrays must have the same length.")
+
+    x_mean = np.mean(x)
+    y_mean = np.mean(y)
+
+    numerator = np.sum((x - x_mean) * (y - y_mean))
+    denominator = np.sqrt(np.sum((x - x_mean) ** 2) * np.sum((y - y_mean) ** 2))
+
+    if denominator == 0:
+        raise ValueError("Standard deviation of input arrays must not be zero.")
+
+    return numerator / denominator