  This work proposes an adaptive trace lasso regularized L1-norm based graph
cut method for dimensionality reduction of Hyperspectral images, called as
`Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this method is to
generate the optimal projection matrix by considering both the sparsity as well
as the correlation of the data samples. The conventional L2-norm used in the
objective function is sensitive to noise and outliers. Therefore, in this work
L1-norm is utilized as a robust alternative to L2-norm. Besides, for further
improvement of the results, we use a penalty function of trace lasso with the
L1GC method. It adaptively balances the L2-norm and L1-norm simultaneously by
considering the data correlation along with the sparsity. We obtain the optimal
projection matrix by maximizing the ratio of between-class dispersion to
within-class dispersion using L1-norm with trace lasso as the penalty.
Furthermore, an iterative procedure for this TL-L1GC method is proposed to
solve the optimization function. The effectiveness of this proposed method is
evaluated on two benchmark HSI datasets.
