MATLAB Implementation of Logistic Regression Algorithm

Logistic regression is a widely used classification algorithm that performs exceptionally well in binary classification problems. Implementing logistic regression in MATLAB can be achieved by writing concise and efficient custom code. The core concept of logistic regression involves mapping the output of linear regression to values between 0 and 1 using the Sigmoid function, thereby obtaining classification probabilities. The training process typically optimizes the loss function (such as cross-entropy loss) using gradient descent, gradually adjusting model parameters to achieve optimal classification performance. When implementing in MATLAB, the code structure should follow this logical flow: First, define the Sigmoid function using an anonymous function like `sigmoid = @(z) 1./(1+exp(-z))` to transform linear combinations into probabilities. Next, initialize model parameters including weights and bias terms, typically as zero vectors or small random values. Then implement an iterative optimization process (such as gradient descent) to adjust parameters by calculating errors between predicted values and true labels, followed by backpropagation to update weights. To enhance computational efficiency, leverage MATLAB's matrix operations by using vectorized calculations instead of explicit loops, significantly speeding up the computation. Additionally, incorporate regularization terms (like L2 regularization) to prevent overfitting by adding a penalty term to the loss function. Implement learning rate adjustment strategies such as adaptive learning rates or decay schedules to improve model convergence. Finally, validate the model using test data and evaluate performance metrics including accuracy, recall, precision, and F1-score through confusion matrix analysis. Compared to using pre-built toolbox functions, writing custom logistic regression code not only facilitates deeper understanding of algorithm principles but also allows flexible adjustment of optimization strategies according to specific requirements while maintaining high computational efficiency. The implementation can be extended to include features like mini-batch gradient descent, early stopping, and multi-class classification using softmax regression.