*Article* **Classification of Hyperspectral Images by SVM Using a Composite Kernel by Employing Spectral, Spatial and Hierarchical Structure Information**

#### **Yi Wang \* and Hexiang Duan**

Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China; dhx12cug@163.com

**\*** Correspondence: cug.yi.wang@gmail.com; Tel.: +86-27-6788-3251

Received: 2 February 2018; Accepted: 27 February 2018; Published: 12 March 2018

**Abstract:** In this paper, we introduce a novel classification framework for hyperspectral images (HSIs) by jointly employing spectral, spatial, and hierarchical structure information. In this framework, the three types of information are integrated into the SVM classifier in a way of multiple kernels. Specifically, the spectral kernel is constructed through each pixel's vector value in the original HSI, and the spatial kernel is modeled by using the extended morphological profile method due to its simplicity and effectiveness. To accurately characterize hierarchical structure features, the techniques of Fish-Markov selector (FMS), marker-based hierarchical segmentation (MHSEG) and algebraic multigrid (AMG) are combined. First, the FMS algorithm is used on the original HSI for feature selection to produce its spectral subset. Then, the multigrid structure of this subset is constructed using the AMG method. Subsequently, the MHSEG algorithm is exploited to obtain a hierarchy consist of a series of segmentation maps. Finally, the hierarchical structure information is represented by using these segmentation maps. The main contributions of this work is to present an effective composite kernel for HSI classification by utilizing spatial structure information in multiple scales. Experiments were conducted on two hyperspectral remote sensing images to validate that the proposed framework can achieve better classification results than several popular kernel-based classification methods in terms of both qualitative and quantitative analysis. Specifically, the proposed classification framework can achieve 13.46–15.61% in average higher than the standard SVM classifier under different training sets in the terms of overall accuracy.

**Keywords:** hyperspectral images (HSIs); classification; SVM; composite kernel; algebraic multigrid methods
