Two-Class Classifier Using LMS, MSE, and Perceptron Criterion Functions

Two-class classifiers are fundamental machine learning algorithms that separate data into two distinct categories using specific decision boundaries. These classifiers implement various optimization approaches including LMS (Least Mean Squares), MSE (Mean Squared Error), and Perceptron criterion functions to achieve accurate binary classification. The LMS algorithm operates as an adaptive filter that minimizes the cost function through gradient descent. In code implementation, the weight update rule follows: w(n+1) = w(n) + η * e(n) * x(n), where η represents the learning rate, e(n) denotes the instantaneous error between predicted and actual values, and x(n) is the input feature vector. This iterative process continues until convergence is achieved. The MSE criterion function calculates the average squared difference between predicted outputs and true labels. The mathematical formulation involves minimizing J(w) = (1/2N)Σ(y_i - w^T x_i)^2 across all training samples. Implementation typically involves batch gradient descent or matrix operations for efficient computation of optimal weights. The Perceptron criterion function employs a threshold-based activation mechanism where the decision function f(x) = sign(w^T x + b) determines class membership. The algorithm updates weights using the rule: w ← w + η * (y_i - ŷ_i) * x_i when misclassification occurs, ensuring linear separability through iterative adjustments. By integrating these complementary approaches, the two-class classifier demonstrates robust performance across various datasets, leveraging LMS for adaptive learning, MSE for error minimization, and Perceptron for linear decision boundary formation to achieve high classification accuracy.