A theoretical performance analysis of the Bayesian data reduction algorithm

The purpose of this paper is to analytically demonstrate the effect that the overall quantization, M, has on the relative performance of the BDRA (Bayesian Data Reduction Algorithm). In particular, it is of interest to show with a straightforward data model how the dimensionality reduction aspects of the BDRA improves overall classification performance on the training data. In other words, it is analytically shown the conditions under which the probability of error, as computed on the data, is lower after dimensionality reduction. Results are illustrated by plotting the analytical probability of error as a function of the number of data merged in the same discrete cell. An interesting result demonstrates that data merged under different classes in the same discrete cell can improve classification performance.