Sparse dimensionality reduction of hyperspectral image based on semi-supervised local Fisher discriminant analysis

- We propose a novel sparse dimensionality reduction method of hyperspectral image based on semi-supervised local Fisher discriminant analysis (SELF).
- The new method is designed to be especially effective for dealing with the out-of-sample extrapolation to realize advantageous complementarities between SELF and sparsity preserving projections (SPP).
- We establish the new objective function to combine SELF and SPP and calculate the objective function using the Lagrange multiplier method.

This paper presents a novel sparse dimensionality reduction method of hyperspectral image based on semi-supervised local Fisher discriminant analysis (SELF). The proposed method is designed to be especially effective for dealing with the out-of-sample extrapolation to realize advantageous complementarities between SELF and sparsity preserving projections (SPP). Compared to SELF and SPP, the method proposed herein offers highly discriminative ability and produces an explicit nonlinear feature mapping for the out-of-sample extrapolation. This is due to the fact that the proposed method can get an explicit feature mapping for dimensionality reduction and improve the classification performance of classifiers by performing dimensionality reduction. Experimental analysis on the sparsity and efficacy of low dimensional outputs shows that, sparse dimensionality reduction based on SELF can yield good classification results and interpretability in the field of hyperspectral remote sensing.