Khatri-Rao Factorization Based Bi-Level Support Vector Machine for Hyperspectral Image Classification

As a benchmark supervised learning algorithm, support vector machine (SVM) has drawn much attention and reported plenty of impressive results in hyperspectral images (HSIs) classification. It builds decision plane with soft margins to divide data into different classes. In previous studies, SVM usually employs a prepared spatial feature to improve its classification performance. Unlike those available where feature and classifier are separately designed, in this study, a bi-level joint optimization framework is developed to bridge SVM classifier training with Gabor feature learning. It is called bi-level support vector machine (BSVM). Inside BSVM, two data-oriented schemes are designed for further enhancement. First, it utilizes Khatri-Rao factorization to reshape the feature learning problem into tensor form which intends to break the feature factor matrix into small pieces and make the problem feasible in computation. Second, it embeds a local regularization term to promote discriminant ability. The normal vector of BSVM and feature factor matrices are solved by alternating iteration. BSVM is validated by extensive experiments on four popular HSI data sets. It achieves 76.10%, 82.84%, 89.04%, and 89.83% in classification accuracy on Houston 2018, Xiong'an, Houston 2013, and Indian Pines respectively, showing significantly improvement over the latest deep learning algorithms and proving its effectiveness and superiority.