PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
January 2017
37
Fusion of Graph Embedding and Sparse
Representation for Feature Extraction and
Classification of Hyperspectral Imagery
Fulin Luo, Hong Huang, Jiamin Liu, and Zezhong Ma
Abstract
The graph embedding algorithms have been widely applied
for feature extraction (
FE
) of hyperspectral imagery (
HSI
). These
methods need to construct a similarity graph with k-nearest
neighbors or
ϵ
-radius ball. However, the neighborhood size is
difficult to select in real-world applications. To solve the prob-
lem, we propose a new unsupervised
FE
method, called sparsity
preserving analysis (
SPA
), based on sparse representation and
graph embedding. The proposed algorithm utilizes sparse
representation to obtain the sparse coefficients of data. Then, it
constructs a new graph with the sparse coefficients that reveals
the sparse properties of data. Finally, the structure of the graph
is preserved in low-dimensional space to obtain a transforma-
tion matrix for
FE
. In addition, a new classification method,
termed sparse neighborhood classifier (
SNC
), is designed using
the sparse representation-based methodology. It uses the sparse
coefficients of a new sample to obtain the similarity weights in
each class. Then, the label information of the new sample is
obtained by the weights. The classification accuracies of
SPA
with
SNC
reach to 86.9 percent and 80.6 percent on PaviaU and
Urban
HSI
data sets, respectively. The results demonstrate that
SPA
with
SNC
can effectively extract low-dimensional features
and improve the discriminating power for
HSI
classification.
Introduction
Hyperspectral imagery (
HSI
) contains hundreds of contigu-
ous bands covering the visible, near-infrared and shortwave
infrared bands (Moreno
et al
., 2014).
HSI
possesses good
discriminating power for similar land cover types (Zhao
et al
.,
2008), and it has been widely applied in the fields of target
detection, resource exploitation, and land cover investigation
(Shao and Zhang, 2014). However, the curse of dimension-
ality is a major challenge for
HSI
classification (Yan and Niu,
2014). Therefore, it is an urgent issue to reduce the number of
bands without loss of information (Villa
et al
., 2013).
Feature extraction (
FE
) is an effective way to map the data
from an original space to a low-dimensional space by preserv-
ing some desired information. Principal component analysis
(
PCA
) and minimum noise fraction (
MNF
) are two classic
FE
methods. These methods are on the basis of statistics and
cannot reveal the intrinsic structure of data (Han
et al
., 2013).
However, Bachmann
et al
. (2005) has discovered the mani-
fold structure in
HSI
data. Recently, many manifold learning
algorithms have been proposed to analyze high-dimensional
data that lies on or near a low-dimensional manifold. Such
methods include locally linear embedding (Roweis and Saul,
2000), Laplacian eigenmaps (Belkin and Niyogi, 2003), neigh-
borhood preserving embedding (
NPE
) (He
et al
., 2005), locality
preserving projections (
LPP
) (He and Niyogi, 2004). For better
understanding of these methods, Yan
et al
. (2007) proposed
a graph embedding framework to unify these methods. Their
differences lie in the way to construct a similarity matrix and a
constraint matrix. The traditional method for graph construc-
tion is based on
k
-nearest neighbors or
ϵ
-radius ball. However,
the value of
k
or ϵ is datum-dependent and difficult to obtain a
proper value in real-world applications (Huang
et al
., 2015).
In recent years, sparse representation gives rise to the
attention of many researchers (Wright
et al
., 2009). Sparse
representation contains the natural discriminating power to
obtain some significant features, and it has been widely ap-
plied in signal processing, statistics, and image classification
(Sun
et al
., 2013). Many sparse representation methods have
been proposed including sparse principal component anal-
ysis (
SPCA
) (Zou
et al
., 2006), sparsity preserving projections
(
SPP
) (Qiao
et al
., 2010) and sparse neighborhood preserving
embedding (Sparse
NPE
) (Cheng
et al
., 2010). Shi
et al
. (2010)
proposed a framework integrating graph embedding into
sparse regression model that improves the representation of
embedding features. In fact, Sparse
NPE
is identical to
SPP
.
They construct a specific graph and the edge weights of the
graph are derived by solving an
ℓ
1
-norm optimization prob-
lem. The graph is insensitive to data noise and inherits many
advantages of sparse representation (Ly
et al
., 2014).
In this paper, we propose a novel unsupervised
FE
method,
termed sparsity preserving analysis, based on graph embed-
ding and sparse representation.
SPA
constructs an adaptive
graph with sparse coefficients obtained from sparse represen-
tation. It not only inherits many merits of sparse representa-
tion but also preserves the manifold structure of data.
SPA
can
effectively extract the discriminating features of high-dimen-
sional data. In addition, a new classification algorithm, called
sparse neighborhood classifier (
SNC
), is presented with sparse
representation. It computes the similarity weights in each
class by using sparse coefficients to obtain the label informa-
tion of new samples. As a result,
SPA
and
SNC
improve the
performance of
HSI
classification compared to many tradition-
al
FE
methods and classifiers.
The remainder of the paper is organized as follows. In
the next section , we review briefly graph embedding and
SPP
;
SPA
and
SNC
are then introduced in the two following
Sections. Then, experimental results are presented to demon-
strate the effectiveness of
SPA
and
SNC
, followed by conclud-
ing remarks and suggestions for future work.
Fulin Luo, Hong Huang, and Jiamin Liu are with Key Labo-
ratory of Optoelectronic Technology and Systems of the Ed-
ucation Ministry of China, Chongqing University, Chongqing
400044, China (
).
Zezhong Ma is with Chongqing Institute of Surveying and
Planning for Land, Chongqing 400020, China.
Photogrammetric Engineering & Remote Sensing
Vol. 83, No. 1, January 2017, pp. 37–46.
0099-1112/17/37–46
© 2017 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.83.1.37
