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Benois-Pineau, J., Khrennikov, A.Y. and Kotovich, N.V. (2001) Segmentation of Images in p-Adic and Euclidean Metrics. Doklady Mathematic, 64, 450-455.

has been cited by the following article:

• TITLE: Finding the Asymptotically Optimal Baire Distance for Multi-Channel Data

  AUTHORS: Patrick Erik Bradley, Andreas Christian Braun

  KEYWORDS: p-Adic Numbers, Ultrametrics, Baire Distance, Support Vector Machine, Classification

  JOURNAL NAME: Applied Mathematics, Vol.6 No.3, March 10, 2015

  ABSTRACT: A novel permutation-dependent Baire distance is introduced for multi-channel data. The optimal permutation is given by minimizing the sum of these pairwise distances. It is shown that for most practical cases the minimum is attained by a new gradient descent algorithm introduced in this article. It is of biquadratic time complexity: Both quadratic in number of channels and in size of data. The optimal permutation allows us to introduce a novel Baire-distance kernel Support Vector Machine (SVM). Applied to benchmark hyperspectral remote sensing data, this new SVM produces results which are comparable with the classical linear SVM, but with higher kernel target alignment.