IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 60, 2022 5500517 Dual Sparse Representation Graph-Based Copropagation for Semisupervised Hyperspectral Image Classification Youqiang Zhang , Member, IEEE, Guo Cao , Bisheng Wang, Xuesong Li , Prince Yaw Owusu Amoako, and Ayesha Shafique Abstract— Graph-based semisupervised hyperspectral image (HSI) classification methods have obtained extensive attention. In graph-based methods, a graph is first constructed, and then the label propagation is carried out on the constructed graph to obtain the labels for unknown samples. However, the results of label propagation may be unreliable, especially in the case of very limited labeled samples. To address the above problem, we pro- pose dual sparse representation graph-based collaborative prop- agation (DSRG-CP) for HSI classification. Specifically, DSRG-CP adopts sparse representation (SR) to construct spectral and spa- tial graphs on spectral and spatial dimensions, respectively. Then, label propagation is performed on two graphs iteratively. In each iteration, only the samples with high classification confidence from one graph are added into another graph as labeled samples for the next label propagation. After several iterations, the labels of unlabeled samples are predicted by fusing the results of label propagation from two graphs. In addition, to make the spectral graph more discriminative, the regularizer of spectral statistical information is added into spectral SR model. To make the classification results more consistent in space, the superpixel block constraint is added into spatial graph model as regularizer. To evaluate the performance of the proposed method, DSRG-CP is compared with several graph-based methods and other state- of-the-art methods. Extensive experiments on real HSI data sets show that DSRG-CP can obtain competitive results for HSI classification. Index Terms— Collaborative propagation (copropagation), hyperspectral image (HSI) classification, semisupervised learning (SSL), sparse representation (SR) graph. Manuscript received July 19, 2020; revised November 19, 2020; accepted December 18, 2020. Date of publication January 8, 2021; date of current version December 3, 2021. This work was supported in part by the Start Foun- dation of Nanjing University of Posts and Telecommunications (NUPTSF) under Grant NY220157, in part by the Natural Science Foundation of Jiangsu Province under Grant BK20191284, and in part by the National Natural Science Foundation of China under Grant 61801222. (Corresponding author: Guo Cao.) Youqiang Zhang is with the School of Internet of Things, Nanjing University of Posts and Telecommunications, Nanjing 210003, China, and also with the Jiangsu Key Laboratory of Broadband Wireless Communication and Internet of Things, Nanjing University of Posts and Telecommunications, Nanjing 210003, China (e-mail: zhangyouqiang@foxmail.com). Guo Cao, Xuesong Li, Prince Yaw Owusu Amoako, and Ayesha Shafique are with the School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China (e-mail: caoguo@ njust.edu.cn; cedar_xuesong@163.com; 719106020081@njust.edu.cn; ayeshashafique1@gmail.com). Bisheng Wang is with the School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China, and also with the Institute of Computer Graphics and Vision, Graz University of Technology, Graz 8010, Austria (e-mail: 316106002478@njust.edu.cn). Digital Object Identifier 10.1109/TGRS.2020.3046780 I. I NTRODUCTION C LASSIFICATION is an essential task of hyperspec- tral image (HSI) analysis. In the past few years, many supervised methods, such as k -nearest neighbors (k NNs) [1], [2], support vector machines (SVMs) [3], [4], sparse representation-based classifiers (SRCs) [2], [5], extreme learning machines (ELMs) [6], [7], and random forests (RFs) [8], [9], were widely used for HSI classification. These methods are faced with the imbalance between limited labeled samples and high dimensionality of hyperspectral data, which easily result in Hughes phenomenon [10]. Semisupervised learning (SSL) methods [11] provide promising solutions to address the above problem. Several SSL methods have been successfully used for HSI classification, which are categorized into five classes: 1) self-training [12], [13]; 2) generative mod- els [14]; 3) transductive SVM (TSVM) [15]; 4) graph-based methods [16], [17]; and 5) cotraining [18], [19]. Our work concentrates on graph-based approaches, which have achieved great success in HSI classification [16], [17], [20]–[29]. There are two important parts of graph-based SSL. One is the construction of the graph, where the vertices in the graph represent data points (both unlabeled and labeled), and the edge weights indicate the similarities between pair- wise samples. The other is propagating the labels from labeled samples to unlabeled samples via the graph. Tra- ditional graph-based SSL methods generally use k NN or ε-ball neighborhood to obtain the adjacency matrix of the graph, then several different ways such as Gaussian kernel (GK) function [16], [21], [30], [31], local manifold learn- ing (LML) [22], [24], and local linear reconstruction (LLR) [32], [33] are adopted to obtain the edge weights. Recently, sparse representation (SR) was introduced to construct graph-based semisupervised HSI classification mod- els [23], [26], [28]. Cheng et al. [34] and Yan and Wang [35] first used SR to construct l 1 -graphs, where the similarities among samples are measured by solving l 1 optimization. Then, SR graph-based SSL methods were used for HSI classification. For example, Gu and Feng [36] firstly used l 1 -graph for semisupervised HSI classification. Shao et al. [23] proposed to utilize a probabilistic class structure to regularize the SR graph. Shao et al. [26] also adopted spatial information to regularize the SR graph. In addition, SR graphs were used for discriminant analysis of HSIs [37], [38]. SR graph has a solid mathematical background, and it can determine the graph 1558-0644 © 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on April 19,2023 at 06:24:11 UTC from IEEE Xplore. Restrictions apply.