Building classification algorithm based on combining the improved principal component analysis and fuzzy relationship of Bayesian method

This article develops a novel classification algorithm that integrates the improved Bayesian approach with Principal Component Analysis (PCA). First, PCA significantly reduces the dimensionality of the data while enhancing inter-class separability, thereby improving classification performance. Next, the prior probabilities are refined based on newly derived variables established for both the training and test sets using a fuzzy clustering analysis technique. Finally, the Bayesian classification rule is constructed based on the probability density functions of the classes, using the transformed variables obtained from PCA and the estimated prior probabilities. The algorithm is presented in detail, including procedural steps, illustrative example, and implementation on both numerical and image data through a the establised RStudio procedure. A key contribution of this study lies in the theoretical enhancement of Bayes error analysis and the proof of convergence of the proposed algorithm. Empirical applications demonstrate that the proposed algorithm yields stable results and outperforms several existing approaches when applied to certain numerical and image datasets using statistical parameters.

کلیدواژه ها:

Bayesian classifier ، fuzzy relationship ، Image analysis ، posterior probability ، Principal component analysis