UL-Isomap based nonlinear dimensionality reduction for hyperspectral imagery classification

The paper proposes an upgraded landmark-Isometric mapping (UL-Isomap) method to solve the two problems of landmark selection and computational complexity in dimensionality reduction using landmark Isometric mapping (LIsomap) for hyperspectral imagery (HSI) classification. First, the vector quantization method is introduced to select proper landmarks for HSI data. The approach considers the variations in local density of pixels in the spectral space. It locates the unique landmarks representing the geometric structures of HSI data. Then, random projections are used to reduce the bands of HSI data. After that, the new method incorporates the Recursive Lanczos Bisection (RLB) algorithm to construct the fast approximate k-nearest neighbor graph. The RLB algorithm accompanied with random projections improves the speed of neighbor searching in UL-Isomap. After constructing the geodesic distance graph between landmarks and all pixels, the method uses a fast randomized low-rank approximate method to speed up the eigenvalue decomposition of the inner-product matrix in multidimensional scaling. Manifold coordinates of landmarks are then computed. Manifold coordinates of non-landmarks are computed through the pseudo inverse transformation of landmark coordinates. Five experiments on two different HSI datasets are run to test the new UL-Isomap method. Experimental results show that UL-Isomap surpasses LIsomap, both in the overall classification accuracy (OCA) and in computational speed, with a speed over 5 times faster. Moreover, the UL-Isomap method, when compared against the Isometric mapping (Isomap) method, obtains only slightly lower OCAs.