added self organising maps algorithm in the machine learning section. (#6877)

* added self organising maps algo

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* Update machine_learning/Self_Organising_Maps.py

* Update and rename Self_Organising_Maps.py to self_organizing_map.py

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* Update self_organizing_map.py

* Update self_organizing_map.py

* Update self_organizing_map.py

* Update self_organizing_map.py

Co-authored-by: Eeman Majumder <eemanmajumder@Eemans-MacBook-Pro.local>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

Author: 4 people

machine_learning/self_organizing_map.py

@@ -0,0 +1,73 @@
+"""
+https://en.wikipedia.org/wiki/Self-organizing_map
+"""
+import math
+
+
+class SelfOrganizingMap:
+    def get_winner(self, weights: list[list[float]], sample: list[int]) -> int:
+        """
+        Compute the winning vector by Euclidean distance
+
+        >>> SelfOrganizingMap().get_winner([[1, 2, 3], [4, 5, 6]], [1, 2, 3])
+        1
+        """
+        d0 = 0.0
+        d1 = 0.0
+        for i in range(len(sample)):
+            d0 += math.pow((sample[i] - weights[0][i]), 2)
+            d1 += math.pow((sample[i] - weights[1][i]), 2)
+            return 0 if d0 > d1 else 1
+        return 0
+
+    def update(
+        self, weights: list[list[int | float]], sample: list[int], j: int, alpha: float
+    ) -> list[list[int | float]]:
+        """
+        Update the winning vector.
+
+        >>> SelfOrganizingMap().update([[1, 2, 3], [4, 5, 6]], [1, 2, 3], 1, 0.1)
+        [[1, 2, 3], [3.7, 4.7, 6]]
+        """
+        for i in range(len(weights)):
+            weights[j][i] += alpha * (sample[i] - weights[j][i])
+        return weights
+
+
+# Driver code
+def main() -> None:
+    # Training Examples ( m, n )
+    training_samples = [[1, 1, 0, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 0, 1, 1]]
+
+    # weight initialization ( n, C )
+    weights = [[0.2, 0.6, 0.5, 0.9], [0.8, 0.4, 0.7, 0.3]]
+
+    # training
+    self_organizing_map = SelfOrganizingMap()
+    epochs = 3
+    alpha = 0.5
+
+    for i in range(epochs):
+        for j in range(len(training_samples)):
+
+            # training sample
+            sample = training_samples[j]
+
+            # Compute the winning vector
+            winner = self_organizing_map.get_winner(weights, sample)
+
+            # Update the winning vector
+            weights = self_organizing_map.update(weights, sample, winner, alpha)
+
+    # classify test sample
+    sample = [0, 0, 0, 1]
+    winner = self_organizing_map.get_winner(weights, sample)
+
+    # results
+    print(f"Clusters that the test sample belongs to : {winner}")
+    print(f"Weights that have been trained : {weights}")
+
+
+# running the main() function
+if __name__ == "__main__":
+    main()