MATLAB Implementation of Bayesian Classification

Bayesian classification is a probability-based machine learning method that utilizes Bayes' theorem to calculate the probability of a sample belonging to a specific category. Implementing Bayesian classification in MATLAB typically involves the following key steps.

First, you need to prepare training data. Data is usually stored in matrix format, where each row represents a sample and each column represents a feature. You also need corresponding class label vectors indicating which category each sample belongs to. In MATLAB code, this can be implemented using data matrices and categorical arrays.

Second, calculate prior probabilities. Prior probability refers to the probability of each category occurring without observing sample features. This can be estimated by counting the frequency of each category in the training data using MATLAB's histcounts or grpstats functions.

Next, compute conditional probabilities. The core of Bayesian classification lies in calculating the probability distribution of features given each category. For continuous features, we typically assume a Gaussian distribution and calculate its mean and variance using mean and var functions. For discrete features, we directly count their frequency distribution with histcounts or accumarray.

Then, perform classification using Bayes' theorem. For new test samples, compute their posterior probability for each category, combining prior probabilities and conditional probabilities to determine the most likely category. The category with the highest posterior probability becomes the prediction result. This can be implemented using probability multiplication and max function operations.

Finally, evaluate classification performance. You can use metrics like confusion matrices, accuracy, and recall rates to measure classifier performance. MATLAB provides built-in functions such as confusionmat and perfcurve for performance evaluation.

MATLAB offers Statistics and Machine Learning Toolbox with built-in functions like fitcnb for training naive Bayes classifiers. By adjusting parameters, such as selecting different distribution assumptions (Gaussian, multinomial, etc.), you can optimize classification performance through the DistributionNames parameter.

This classification method is simple and efficient, particularly suitable for text classification and spam filtering problems. However, it's important to note that if features have strong correlations, the performance of naive Bayes (which assumes feature independence) may be affected. In such cases, consider using more complex Bayesian network models available in MATLAB's Bayesian Network Toolbox.