MATLAB Implementation of Naive Bayes Classification

Naive Bayes classification is a simple probabilistic classifier based on Bayes' theorem, which operates under the assumption of feature independence. Implementing this algorithm in MATLAB primarily involves two core components: probability calculation and classification decision-making.

The implementation begins with preparing a training dataset containing feature vectors and corresponding class labels. During the training phase, the algorithm calculates two key probabilities: prior probability and conditional probability. The prior probability represents the frequency of each class occurrence in the training set, while conditional probability describes the distribution of each feature under different classes.

For continuous features, the implementation typically assumes a Gaussian distribution, requiring calculation of mean and variance for each feature within every class. During classification, these statistical measures are used to compute posterior probabilities for test samples belonging to each class, with the final prediction being the class with the highest probability.

Important implementation considerations include handling numerical underflow through logarithmic transformation, where probability multiplication is converted to summation of log probabilities. MATLAB's matrix operation capabilities enable efficient statistical computations, particularly enhancing performance for large datasets through vectorized operations.

This MATLAB implementation finds applications in text classification, spam filtering, medical diagnosis, and various other domains. Its simplicity and efficiency make it an essential algorithm for machine learning beginners, with potential extensions including different distribution assumptions for various data types.