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1320 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 11, NO. 8, AUGUST 2014

Hyperspectral Image Classiﬁcation Using Kernel

Sparse Representation and Semilocal

Spatial Graph Regularization

Jianjun Liu, Zebin Wu, Le Sun, Zhihui Wei, and Liang Xiao

Abstract—This letter presents a postprocessing algorithm for

a kernel sparse representation (KSR)-based hyperspectral image

classiﬁer, which is based on the integration of spatial and spectral

information. A pixelwise KSR is ﬁrst used to ﬁnd the sparse

coefﬁcient vectors of the hyperspectral image. Then, a sparsity

concentration index (SCI) rule-guided semilocal spatial graph

regularization (SSG), called SSG+SCI, is proposed to determine

reﬁned sparse coefﬁcient vectors that promote spatial continuity

within each class. Finally, these reﬁned coefﬁcient vectors are

used to obtain the ﬁnal classiﬁcation map. Compared with pre-

vious approaches based on similar spatial–spectral postprocessing

strategies, SSG+SCI clearly outperforms their results in terms of

accuracy and the number of training samples, as it is demon-

strated with two real hyperspectral images.

Index Terms—Graph regularization, hyperspectral image clas-

siﬁcation, kernel sparse representation (KSR), sparsity concentra-

tion index (SCI).

I. INTRODUCTION

YPERSPECTRAL imaging sensors capture digital im-

ages in hundreds of narrow and contiguous spectral bands

spanning the visible to infrared spectrum. The wealth of spec-

tral information promotes the development of many application

domains, such as military, agriculture, and mineralogy. Among

these applications, image classiﬁcation is an important one

where pixels are labeled to one of the classes. Various methods

have been developed for hyperspectral image classiﬁcation and

have shown a good performance, such as support vector ma-

chines (SVMs) [1], [2], multinomial logistic regression (MLR)

[3], and sparse representation (SR) [4].

Recent work has highlighted that hyperspectral image classi-

ﬁcation should not only focus on analyzing spectral features but

also incorporate information on the spatially adjacent pixels.

Manuscript received July 1, 2013; revised September 24, 2013 and November

4, 2013; accepted November 18, 2013. Date of publication December 20,

2013; date of current version March 11, 2014. This work was supported

in part by the National Natural Science Foundation of China under Grants

61101194, 61071146, and 61171165, by the Jiangsu Provincial Natural Science

Foundation of China under Grant BK2011701, by the Research Fund for the

Doctoral Program of Higher Education of China under Grant 20113219120024,

by the Jiangsu Province Six Top Talents Project of China under Grant WLW-

011, by the CAST Innovation Foundation under Grant CAST201227, and by

the Project of China Geological Survey under Grant 1212011120227.

The authors are with the School of Computer Science and Engineer-

ing, Nanjing University of Science and Technology, Nanjing 210094, China

(e-mail: liuofﬁcial@163.com; zebin.wu@gmail.com; sunlecncom@163.com;

gswei@mail.njust.edu.cn; xiaoliang@mail.njust.edu.cn).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/LGRS.2013.2292831

Generally, the spatial–spectral classiﬁcation methods can be

classiﬁed into two groups. The ﬁrst one can be considered as the

preprocessing methods, where spatial contextual information is

exploited in the classiﬁcation stage. In [2], Camps-Valls et al.

combine spectral and spatial information within a feature vector

of each pixel by taking advantage of the composite kernels and

then apply a pixelwise SVM to the obtained set of vectors.

Gurram and Kwon [5] exploit both local spectral and spatial

information by weighing the neighboring pixels during Hilbert

space embedding and then build a large-margin SVM on the

weighted means of small patches of pixels. The second group is

composed by the algorithms in which the spatial dependence is

exploited at a postprocessing stage. An example is a pixelwise

classiﬁcation followed by Markov random ﬁeld regularization

of the classiﬁcation map [3], [6].

Kernel SR (KSR), a kernel version of SR, has been suc-

cessfully applied to face recognition and hyperspectral image

classiﬁcation recently [7], [8]. Unlike SVM, KSR is a non-

parametric learning method, which does not need a set of hy-

pothesis functions to learn the weight vectors of the hypothesis

function. KSR can be treated as a learning machine in which

the classiﬁcation process is implemented by using the signal

reconstruction methods.

This letter concentrates on KSR. Nevertheless, KSR is a

pixelwise classiﬁcation method without considering the corre-

lations between spatially adjacent pixels. As pointed earlier,

two categories of methods can be used to incorporate spatial

information. For the ﬁrst one, a common approach is to use the

composite kernel framework [8]. For the second one, until now,

there are no related approaches. Different from the classiﬁers

such as MLR and probabilistic SVM (PSVM) [9], the output

of KSR is the sparse coefﬁcient vectors, while the outputs

of MLR and PSVM are the probabilistic classiﬁcation maps.

Spatial smoothness is the main assumption for spatial–spectral

classiﬁcation of hyperspectral images, which assumes that the

neighboring pixels consist of the same type of materials ( same

class) and have similar spectral characteristics. In [10], the

Local Invariance Assumption (LIA) is imposed as follows:

If two pixels are close in the intrinsic geometry of the data

distribution, then the coding vectors of these two pixels with

respect to the new basis are also close to each other. Based

on LIA, the spatial s mooth assumption is also suitable for

the sparse coefﬁcient vectors, since all pixels s hare the same

basis (training dictionary) in KSR. Therefore, the neighboring

coefﬁcient vectors are similar to each other.

Graph-based methods are commonly used in image classi-

ﬁcation problems [10]–[12]. These methods rely on deﬁning

IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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