kNN algorithm based on axis characteristic on Lorentzian space

Lorentzian space is used in Mathematics and Physics. This space has also potential applications in pattern recognition because of its special characteristics. Lorentz space has different characteristics and different inner product definition than Euclidean space; therefore distances between points are calculated in a different way. In this study, contribution of this space to the classification problem has been studied by using its characteristics. For this purpose, kNN algorithm is used as a reference. In order to use this algorithm on Lorentzian space, Lorentzian and Euclidean distance metrics are tried. Factors that influence the success rate of this method, are investigated; and it is found that placing the points on Lorentzian space in an appropriate angle has positive effects. For placing points in an optimum angle and finding the best axis, both Euclidean and Lorenzian (hyperbolic) rotations are applied.