An Augmented Value Difference Measure

• In order to relax the attribute independence assumption by VDM, we proposed an augmented MBR transform.
• Based on our augmented MBR transform, we then proposed an Augmented Value Difference Measure (AVDM).
• The experimental results on a large number of UCI datasets validate its effectiveness.

How to learn distances from categorical variables (nominal attributes) is a key problem in instance-based learning and other paradigms of machine learning. Recent work in distance learning has shown that a surprisingly simple Value Difference Metric (VDM), with strong assumptions of independence among attributes, is competitive with state-of-the-art distance functions such as Short and Fukunaga Metric (SFM) and Minimum Risk Metric (MRM). This fact raises the question of whether a distance function with less restrictive assumptions can perform even better. In order to answer this question, we proposed an augmented memory-based reasoning (MBR) transform. Based on our augmented MBR transform, we then developed an Augmented Value Difference Measure (AVDM) for learning distances from categorical variables. We experimentally tested our AVDM using 36 natural domains and three artificial Monk’s domains, taken from the University of California at Irvine repository, and compared it to its competitor such as VDM, SFM, MRM, ODVDM, and MSFM. The compared results show that our AVDM can generally improve accuracy in domains that involve correlated attributes without reducing accuracy in ones that do not.