Abstract
Semisupervised learning is an effective technique to represent the intrinsic features of a hyperspectral image (HSI), which can reduce the cost to obtain the labeled information of samples. However, traditional semisupervised learning methods fail to consider multiple properties of an HSI, which has restricted the discriminant performance of feature representation. In this article, we introduce the hypergraph into semisupervised learning to reveal the complex multistructures of an HSI, and construct a semisupervised discriminant hypergraph learning (SSDHL) method by designing an intraclass hypergraph and an interclass graph with the labeled samples. SSDHL constructs an unsupervised hypergraph with the unlabeled samples. In addition, a total scatter matrix is used to measure the distribution of the labeled and unlabeled samples. Then, a low-dimensional projection function is constructed to compact the properties of the intraclass hypergraph and the unsupervised hypergraph, and simultaneously separate the characteristics of the interclass graph and the total scatter matrix. Finally, according to the objective function, we can obtain the projection matrix and the low-dimensional features. Experiments on three HSI data sets (Botswana, KSC, and PaviaU) show that the proposed method can achieve better classification results compared with a few state-of-the-art methods. The result indicates that SSDHL can simultaneously utilize the labeled and unlabeled samples to represent the homogeneous properties and restrain the heterogeneous characteristics of an HSI.
Highlights
A HYPERSPECTRAL image (HSI) is composed of tens or hundreds of consecutive narrow electromagnetic bands covering the visible-to-infrared spectrums [1], [2]
For an hyperspectral image (HSI) data set, the labeled samples are denoted as Xl = [xl,1, xl,2, . . . , xl,nl ] ∈ RB×nl and the unlabeled samples are denoted as Xu = [xu,1, xu,2, . . . , xu,nu ] ∈ RB×nu, where B is the number of bands and nl and nu are the numbers of labeled and unlabeled samples, respectively. ∈ {1, 2, . . . , c} is the class label of xl,i, where c is the number of classes
For semisupervised discriminant hypergraph learning (SSDHL), the local information is represented with the intraclass and unsupervised hypergraphs, whereas the global information is described with the interclass graph and the total scatter matrix
Summary
A HYPERSPECTRAL image (HSI) is composed of tens or hundreds of consecutive narrow electromagnetic bands covering the visible-to-infrared spectrums [1], [2]. LUO et al.: SEMISUPERVISED HYPERGRAPH DISCRIMINANT LEARNING FOR DIMENSIONALITY REDUCTION OF HYPERSPECTRAL IMAGE preserving embedding (NPE) [20] and locality preserving projections (LPP) [21], respectively To generalize these methods, a unified graph framework was developed to represent these DR models [22]. For an HSI, the spatial-spectral information was used to construct different spatial-spectral hypergraph models, including spatial hypergraph (SH) [40], hypergraph embedding based spatialspectral joint features (SSHG) [42], and spatial-spectral hypergraph discriminant analysis (SSHGDA) [43] These hypergraph methods cannot utilize the labeled and unlabeled samples to construct effective DR models, simultaneously.
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