Fractional Norms and Quasinorms Do Not Help to Overcome the Curse of Dimensionality.

ABSTRACT: The curse of dimensionality causes the well-known and widely discussed problems for machine learning methods. There is a hypothesis that using the Manhattan distance and even fractional lp quasinorms (for p less than 1) can help to overcome the curse of dimensionality in classification problems. In this study, we systematically test this hypothesis. It is illustrated that fractional quasinorms have a greater relative contrast and coefficient of variation than the Euclidean norm l2, but it is shown that this difference decays with increasing space dimension. It has been demonstrated that the concentration of distances shows qualitatively the same behaviour for all tested norms and quasinorms. It is shown that a greater relative contrast does not mean a better classification quality. It was

SUBMITTER: Mirkes EM 

PROVIDER: S-EPMC7597215 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature