Modified Tensor Locality Preserving Projection for Dimensionality Reduction of Hyperspectral Images

By considering the cubic nature of hyperspectral image (HSI) to address the issue of the curse of dimensionality, we have introduced a tensor locality preserving projection (TLPP) algorithm for HSI dimensionality reduction and classification. The TLPP algorithm reveals the local structure of the original data through constructing an adjacency graph. However, the hyperspectral data are often susceptible to noise, which may lead to inaccurate graph construction. To resolve this issue, we propose a modified TLPP (MTLPP) via building an adjacency graph on a dual feature space rather than the original space. To this end, the region covariance descriptor is exploited to characterize a region of interest around each hyperspectral pixel. The resulting covariances are the symmetric positive definite matrices lying on a Riemannian manifold such that the Log-Euclidean metric is utilized as the similarity measure for the search of the nearest neighbors. Since the defined covariance feature is more robust against noise, the constructed graph can preserve the intrinsic geometric structure of data and enhance the discriminative ability of features in the low-dimensional space. The experimental results on two real HSI data sets validate the effectiveness of our proposed MTLPP method.