Naive Bayes Classifier

The Naive Bayes classifier is a simple probabilistic classifier based on Bayes' theorem, which operates under the assumption that features are mutually independent (the "naive" assumption). Although this assumption rarely holds true in real-world scenarios, Naive Bayes performs remarkably well in practical applications, particularly in text classification and spam filtering domains.

Implementing a Naive Bayes classifier in MATLAB typically involves the following steps:

Data Preparation: Begin by splitting the dataset into training and testing sets. The training set is used to build the probability model, while the testing set evaluates classifier performance. MATLAB's cvpartition function can help create stratified splits for balanced data distribution.

Prior Probability Calculation: Compute the frequency of each class occurrence in the training set to establish class prior probabilities. For example, with two classes A and B, calculate P(A) and P(B). This can be implemented using MATLAB's grpstats or basic frequency counting operations.

Conditional Probability Computation: For each feature, calculate conditional probabilities given specific classes. For continuous features, assume Gaussian distribution and compute mean (mean) and variance (var); for discrete features, use frequency counting. MATLAB's fitcnb automatically handles different distribution types through its 'DistributionNames' parameter.

New Sample Prediction: For test samples, apply Bayes' theorem to compute posterior probabilities for each class, selecting the class with maximum probability as the prediction result. The prediction phase involves probability multiplication and comparison operations.

Model Evaluation: Assess classifier performance using metrics like accuracy, recall, or confusion matrices. MATLAB provides confusionmat and perfcurve functions for comprehensive evaluation.

In MATLAB, the built-in fitcnb function (for classification learning) enables rapid Naive Bayes model construction. This function supports different distribution assumptions (Gaussian, multinomial, etc.) and allows parameter tuning for performance optimization through options like 'OptimizeHyperparameters'.

Naive Bayes classifiers are computationally efficient and easy to implement, making them suitable for high-dimensional data. However, practitioners should be aware of potential biases introduced by the feature independence assumption. In practical applications, performance can be further enhanced through feature selection techniques or ensemble learning methods like fitcensemble in MATLAB.