A Trace Lasso Regularized L1-norm Graph Cut for Highly Correlated Noisy Hyperspectral Image

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.