Author(s)

Patrick Erik Bradley¹, Andreas Christian Braun²

¹Institute of Photogrammetry and Remote Sensing, Karlsruhe Institute of Technology, Karlsruhe, Germany.
²Remote Sensing and Landscape Information Systems, University of Freiburg, Freiburg, Germany.

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.

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

Bradley, P. and Braun, A. (2015) Finding the Asymptotically Optimal Baire Distance for Multi-Channel Data. Applied Mathematics, 6, 484-495. doi: 10.4236/am.2015.63046.