Multiple one-dimensional embedding clustering scheme for hyperspectral image classification

In this paper, we present a novel multiple 1D-embedding based clustering (M1DEBC) scheme for hyperspectral image (HSI) classification. This novel clustering scheme is an iteration algorithm of 1D-embedding based regularization, which is first proposed by J. Wang [Semi-supervised learning using ensembles of multiple 1D-embedding-based label boosting, Int. J. Wavelets, Multiresolut. Inf. Process. 14(2) (2016) 33 pp.; Semi- supervised learning using multiple one-dimensional embedding-based adaptive interpolation, Int. J. Wavelets, Multiresolut. Inf. Process. 14(2) (2016) 11 pp.]. In the algorithm, at each iteration, we do the following three steps. First, we construct a 1D multi-embedding, which contains k different versions of 1D embedding. Each of them is realized by an isometric mapping that maps all the pixels in a HSI into a line such that the sum of the distances of adjacent pixels in the original space is minimized. Second, for each 1D embedding, we use the regularization method to find a pre-classifier to give each unlabeled sample a preliminary label. If all of the k different versions of regularization vote the same preliminary label, then we call it a feasible confident sample. All the feasible confident samples and their corresponding labels constitute the auxiliary set. We randomly select a part of the elements from the auxiliary set to construct the newborn labeled set. Finally, we add the newborn labeled set into the labeled sample set. Thus, the labeled sample set is gradually enlarged in the process of the iteration. The iteration terminates until the updated labeled set reaches a certain size. Our experimental results on real hyperspectral datasets confirm the effectiveness of the proposed scheme.