Linear Threshold Classifier with AdaBoost Algorithm Implementation

A linear threshold classifier is a simple binary classification model that determines sample categories using a linear function and a threshold value. When the linear function's output exceeds the threshold, samples are classified as positive; otherwise, they are classified as negative. While structurally straightforward, this classifier may underperform on certain datasets, particularly when dealing with complex data distributions. In code implementation, the linear function typically involves feature weighting (e.g., w*x + b) where parameters can be optimized using gradient descent or analytical solutions.

AdaBoost (Adaptive Boosting) is an ensemble learning method that constructs a strong classifier by combining multiple weak classifiers. Its core algorithm iteratively trains a sequence of weak classifiers while adjusting sample weights in each iteration, giving higher priority to previously misclassified samples. The final prediction aggregates weighted votes from all weak classifiers, significantly enhancing classification performance. Key implementation steps include initializing uniform weights, calculating weighted error rates, and updating weights using exponential loss functions.

Using linear threshold classifiers as base learners for AdaBoost is particularly effective when data exhibits linear separability. During each iteration, AdaBoost trains a new linear threshold classifier with reweighted samples, focusing on challenging instances from previous rounds. The final strong classifier combines predictions through weighted voting, where classifier weights are proportional to their accuracy. In MATLAB, this can be implemented using fitcsvm for linear classifiers and custom loops for weight updates, with vectorization for efficiency.

This approach offers computational efficiency due to the simplicity of linear classifiers, while AdaBoost's ensemble strategy significantly boosts performance. Practical implementation in programming environments like MATLAB leverages built-in optimization tools (e.g., fmincon) for parameter tuning and efficient matrix operations for weight updates. The combined method proves suitable for various real-world binary classification tasks, balancing model interpretability with predictive power through iterative refinement.