Bayesian Classification-based Handwritten Digit Recognition

Bayesian classification is a pattern recognition method based on probability statistics, particularly suitable for multi-classification problems like handwritten digit recognition. This system implements three distinct Bayesian classifier variants, each optimized for different application scenarios with specific code implementations.

The binary feature-based Bayesian classifier converts image data into black-and-white binary features through threshold processing. This approach simplifies computation by calculating the probability of each pixel being black or white, making it ideal for straightforward digit recognition tasks. In code implementation, this typically involves image binarization using Otsu's method followed by probability calculation for each feature dimension.

The minimum error rate Bayesian classifier focuses on overall classification accuracy by calculating posterior probabilities to minimize total classification error probability. As the fundamental implementation of Bayesian decision theory, this method achieves optimal classification when class prior probabilities are known. The algorithm implementation involves computing likelihood functions and prior probabilities from training data, then applying Bayes' theorem for classification decisions.

The minimum risk Bayesian classifier extends the basic algorithm by introducing risk factor concepts. This implementation considers not only classification error probabilities but also cost differences between various error types. For instance, misclassifying digit 1 as 7 might carry higher practical risk than misclassifying it as 3. The code implementation incorporates a risk matrix that defines penalty weights for different misclassification scenarios, enabling more targeted optimization.

In practical applications, these three methods complement each other. The binary feature method offers high computational efficiency suitable for real-time applications. The minimum error rate method pursues maximum accuracy, while the minimum risk method fits scenarios with significant cost differences between misclassifications. Implementation requires attention to feature extraction quality and training data sufficiency, as these factors significantly impact final recognition performance. The system typically includes preprocessing modules for image normalization and feature extraction routines before applying Bayesian classification algorithms.