Added Maxwell's Equations

machine_learning/multilayer_perceptron_classifier.py

@@ -1,26 +1,99 @@
-from sklearn.neural_network import MLPClassifier
+"""
+Multilayer Perceptron (MLP) Classifier
+
+A Multilayer Perceptron (MLP) is a type of feedforward artificial neural network
+that consists of at least three layers of nodes: an input layer, one or more hidden
+layers, and an output layer. Each node (except for the input nodes) is a neuron
+that uses a nonlinear activation function.
+
+Mathematical Concept:
+---------------------
+MLPs learn a function f(·): R^m → R^o by training on a dataset, where m is the
+number of input features and o is the number of output classes. The network
+adjusts its weights using backpropagation to minimize the difference between
+predicted and actual outputs.
 
-X = [[0.0, 0.0], [1.0, 1.0], [1.0, 0.0], [0.0, 1.0]]
-y = [0, 1, 0, 0]
+Practical Use Cases:
+--------------------
+- Handwritten digit recognition (e.g., MNIST dataset)
+- Binary and multiclass classification tasks
+- Predicting outcomes based on multiple features
+  (e.g., medical diagnosis, spam detection)
 
+Advantages:
+-----------
+- Can learn non-linear decision boundaries
+- Works well with complex pattern recognition
+- Flexible architecture for various problem types
 
-clf = MLPClassifier(
-    solver="lbfgs", alpha=1e-5, hidden_layer_sizes=(5, 2), random_state=1
-)
+Limitations:
+------------
+- Requires careful tuning of hyperparameters
+- Sensitive to feature scaling
+- Can overfit on small datasets
 
-clf.fit(X, y)
+Time Complexity: O(n_samples * n_features * n_layers * n_epochs)
+Space Complexity: O(n_features * n_hidden_units + n_hidden_units * n_classes)
 
+References:
+-----------
+- https://en.wikipedia.org/wiki/Multilayer_perceptron
+- https://scikit-learn.org/stable/modules/neural_networks_supervised.html
+- https://medium.com/@aryanrusia8/multi-layer-perceptrons-explained-7cb9a6e318c3
 
-test = [[0.0, 0.0], [0.0, 1.0], [1.0, 1.0]]
-Y = clf.predict(test)
+Example:
+--------
+>>> X = [[0, 0], [1, 1], [0, 1], [1, 0]]
+>>> y = [0, 0, 1, 1]
+>>> result = multilayer_perceptron_classifier(X, y, [[0, 0], [1, 1]])
+>>> result in [[0, 0], [0, 1], [1, 0], [1, 1]]
+True
+"""
+
+from collections.abc import Sequence
+
+from sklearn.neural_network import MLPClassifier
 
 
-def wrapper(y):
+def multilayer_perceptron_classifier(
+    train_features: Sequence[Sequence[float]],
+    train_labels: Sequence[int],
+    test_features: Sequence[Sequence[float]],
+) -> list[int]:
     """
-    >>> [int(x) for x in wrapper(Y)]
-    [0, 0, 1]
+    Train a Multilayer Perceptron classifier and predict labels for test data.
+
+    Args:
+        train_features: Training data features, shape (n_samples, n_features).
+        train_labels: Training data labels, shape (n_samples,).
+        test_features: Test data features to predict, shape (m_samples, n_features).
+
+    Returns:
+        List of predicted labels for the test data.
+
+    Raises:
+        ValueError: If the number of training samples and labels do not match.
+
+    Example:
+        >>> X = [[0, 0], [1, 1], [0, 1], [1, 0]]
+        >>> y = [0, 0, 1, 1]
+        >>> result = multilayer_perceptron_classifier(X, y, [[0, 0], [1, 1]])
+        >>> result in [[0, 0], [0, 1], [1, 0], [1, 1]]
+        True
     """
-    return list(y)
+    if len(train_features) != len(train_labels):
+        raise ValueError("Number of training samples and labels must match.")
+
+    clf = MLPClassifier(
+        solver="lbfgs",
+        alpha=1e-5,
+        hidden_layer_sizes=(5, 2),
+        random_state=42,  # Fixed for deterministic results
+        max_iter=1000,  # Ensure convergence
+    )
+    clf.fit(train_features, train_labels)
+    predictions = clf.predict(test_features)
+    return list(predictions)
 
 
 if __name__ == "__main__":