A Novel Naive Bayesian Approach to Inference with Applications to the MNIST Handwritten Digit Classification

Naive Bayesian approach is an effective method for many data analysis problems such as pattern classification and machine learning. However, it often suffers from the underflow problem when the input data has a high dimension. Such a problem is often addressed by taking logarithms and working in the transformed domain. In this paper we propose a novel approach to this problem based on geometric means and apply it to the classical MNIST handwritten digit classification problem. The results show that it not only achieves satisfactory accuracy but also demonstrates its power of presenting "second best" guesses that are meaningful and useful in the pattern classification domain.