The use of Lorentzian distance metric in classification problems

Abstract

In this paper, we introduce Lorentzian distance metric into classification problem. Here we benefit from the interesting properties of the distance metric of the Lorentzian space. A preprocessing step composed of basic mathematical operations such as compression and shifting is necessary to prepare for using the Euclidean data in the Lorentzian space. For defining validity and usability of this method, 6 public datasets (CLIMATE, GESTURE, PARKINSON, RELAX, VERTEBRAL, WINE) are used in our experiments. The experimental results are compared with k Nearest Neighbor (kNN) and other well-known classification methods. Test results show that our method produces better classification rates in most cases. Furthermore, for increasing the classification rate, we improve our base method with some extensions. We investigate the influence of parameters in compression matrix and obtain optimum values. On the other hand, we add a rotation operation into the preprocessing step. These improvements increase significantly the classification rate.