Maxwell Normal Distribution in a Manifold and Mahalanobis Metric

  • Yukihiko Yamashita
  • Mariko Numakami
  • Naoya Inoue
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4109)


The normal distribution in Euclidean space is used widely for statistical models. However, for pattern recognition, since pattern vectors are often normalized by their norm, they are on a hyper-spherical surface. Therefore, we have to study a normal distribution in a non-Euclidean space. Here, we provide the new concept of geometrically local isotropic independence and define the Maxwell normal distribution in a manifold. We also define the Mahalanobis metric, which is an extension of the Mahalanobis distance in Euclidean space. We provide the Mahalanobis metric equation, which is covariant with coordinate transformation. Furthermore, we show its experimental results.


Riemannian Manifold Euclidean Space Central Limit Theorem Coordinate Transformation Mahalanobis Distance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yukihiko Yamashita
    • 1
  • Mariko Numakami
    • 1
  • Naoya Inoue
    • 1
  1. 1.Graduate School of Science and EngineeringTokyo Institute of TechnologyTokyoJapan

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