A Modified Short and Fukunaga Metric based on the attribute independence assumption

Abstract

It is well known that the naive Bayesian classifier assumes the attribute independence given the class. According to our observation, some distance functions also assume the attribute independence, such as Value Difference Metric (VDM). Short and Fukunaga Metric (SFM) is another widely used distance function, which does not assume the attribute independence. In this paper, we investigate the attribute independence assumption in VDM, and propose a Modified Short and Fukunaga Metric (MSFM) based on the attribute independence assumption. We find that MSFM is surprisingly similar to VDM. In fact, based on some assumptions, our MSFM can be regarded as a logarithmic modification of VDM. That is to say, in some sense, a logarithmic modification of SFM is equivalent to a logarithmic modification of VDM. Our experimental results on a large number of UCI benchmark datasets show that MSFM significantly outperforms SFM and SF2LOG (another improved version of SFM), and almost ties VDM.