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.
Highlights
The Baire distance was introduced to classification in order to produce clusters by grouping data in “bins” by [1]
The Baire distance we use depends on a parapmeter, and we argue that the precise value of this parameter is seldom to be expected of interest
Support Vector Machine (SVM) has been intensely applied for classification tasks in remote sensing and several methodological comparisons have been established in previous work of the authors [9] [10]
Summary
The Baire distance was introduced to classification in order to produce clusters by grouping data in “bins” by [1]. In this way, they seek to find inherent hierarchical structure in data defined by their features. In this paper we introduce a permutation-dependent Baire distance for data with n features, and we define a. For the asymptotically optimal permutation, the resulting Baire distance SVM yields results comparable with the classical linear SVM on the AVIS Indian Pine dataset. The latter is a well known hyperspectral remote sensing dataset. As our preliminary practical result, we obtain greater completeness in many of our clusters than with the classical linear SVM clusters
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