SSMD: Dimensionality Reduction and Classification of Hyperspectral Images Based on Spatial–Spectral Manifold Distance Metric Learning

Metric learning, which aims to obtain a metric matrix M such that samples from the same class are close to one another and samples of different classes are far from one another, is widely used in the field of hyperspectral dimensionality reduction (DR) and classification. Traditional metric learning is based on the Mahalanobis distance, which measures the similarity between samples via point-to-point distance, ignoring the structural features of the hyperspectral images (HSIs). To solve the above problem, we proposed clustered multiple manifold metric learning (CM3L), which obtains a manifold distance (MD), aimed at improving discrimination by introducing structural features of the HSIs and achieving good results. However, this manifold distance still has certain shortcomings in specific application situations. MD only considers the labeled data in the construction of the manifold and ignores the unlabeled data, resulting in the destruction of the manifold. Therefore, this article proposes a new spatial–spectral manifold distance (SSMD) to improve the performance of metric learning in hyperspectral DR and classification by maintaining the integrity of the constructed manifolds. The SSMD selects suitable neighboring points in the labeled and unlabeled data through the spectral–spatial information in order to participate in the construction of the manifold. Then, the distance between the manifolds is calculated to replace the traditional Mahalanobis distance. The results of seven sets of comparison experiments on three real HSI datasets demonstrate the effectiveness of SSMD in improving the classification results of HSIs.