Finding the Asymptotically Optimal Baire Distance for Multi-Channel Data

作     者：Patrick Erik Bradley Andreas Christian Braun 

作者机构：Institute of Photogrammetry and Remote Sensing Karlsruhe Institute of Technology Karlsruhe Germany Remote Sensing and Landscape Information Systems University of Freiburg Freiburg Germany 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2015年第6卷第3期

页      面：484-495页

学科分类：07[理学] 0701[理学-数学] 

主　　题：p-Adic Numbers Ultrametrics Baire Distance Support Vector Machine Classification 

摘      要：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.