Regularized Multinomial Regression Method for Hyperspectral Data Classification via Pathwise Coordinate Optimization

Hyperspectral imagery generally contains enormous amounts of data due to hundreds of spectral bands. As recent researchers have discovered, many of the bands are highly correlated and may provide redundant information for the classification related problems. Therefore, feature selection is very important in hyperspectral image processing problem. ''Pathwise Coordinate Descent'' algorithm is the ''one-at-a-time'' coordinate-wise descent algorithm for a class of convex optimization problems. When applied on the L1-regularized regression (lasso) problem, the algorithm can handle large problems and can also efficiently obtain sparse features in a comparatively very low timing cost. Through computing the solutions for a decreasing sequence of regularization parameters, the algorithm also combines model selection procedure into itself. In this paper, we utilize the multinomial logistic regression with lasso, elastic-net convex penalties on hyperspectral image classification. Pathwise Coordinate Descent is used for estimation these models. Experimental results demonstrate that, in the context of the hyperspectral data classification problem, models obtained by Pathwise Coordinate Descent algorithm do effectively achieve a sparse feature subsets and very good classification results with very low computational costs.