Hyperspectral Image Classification Powered by Khatri-Rao Decomposition-Based Multinomial Logistic Regression

Abstract

Multinomial logistic regression (MLR) is of great significance in hyperspectral image (HSI) classification within remote sensing community. It seeks the optimal regressors with logistic loss function. In the past, spatial information has been widely used to improve its classification performance by means of some prepared feature or postprocessing techniques. To better understand HSI data and learn more effective spatial feature, in this paper, a joint optimization framework which combines MLR classifier training with Khatri-Rao decomposition-based feature learning is proposed for HSI classification. It is called Khatri-Rao decomposition-based multinomial logistic regression algorithm (KR-MLR). With Gabor feature as input, KR-MLR customizes two data-oriented strategies. One is to insert a feature learning layer after the initial input and optimize it with classifier concurrently. Moreover, Khatri-Rao decomposition is utilized to convert the problem into tensor space and make it feasible in computation. Another is to add local regularization term to preserve discriminant information as well. The regressors and feature factor matrices are optimized in iterative fashion. The proposed KR-MLR is investigated on four popular HSI data sets. The experimental results show that KR-MLR outperforms other prior arts, proving it a competitive and promising classifier.