Least Squares Method Implementation for Binary Classification

In this article, we demonstrate how to implement the least squares method using MATLAB to achieve correct classification between two categories. The least squares method is a mathematical optimization technique that finds a line or curve that best fits a set of data points by minimizing the sum of squared residuals. For classification purposes, we employ this method to determine an optimal separation boundary that minimizes misclassification between the two classes. The implementation involves several key MATLAB functions and algorithmic steps: First, we organize the training data into feature matrices and label vectors. The core computation uses MATLAB's matrix operations to solve the normal equations (X'X)\X'y, where X represents the feature matrix and y contains the class labels. This yields the optimal weight vector that defines the classification boundary. We provide code examples showcasing how to handle both linear and polynomial decision boundaries. The implementation includes error handling for singular matrices using MATLAB's pseudoinverse function (pinv) and demonstrates how to calculate classification accuracy by comparing predicted labels against actual labels. The code also visualizes the decision boundary using MATLAB's plotting functions, allowing users to intuitively understand the classification performance.