Hyperspectral Image Classification using One
Dimensional Manifold Embedding with
Spectral-Spatial based Affinity Metric
Huiwu Luo
∗
, Yuan Yan Tang
∗
, Yulong Wang
∗
,
Chunli Li
∗
, Jianzhong Wang
†
, Tingbo Hu
‡
and Hong Li
§
∗
University of Macau, Macau, China
Email: luohuiwu@gmail.com; yytang@umac.mo; wangyulong6251@gmail.com; mb35457@umac.mo
†
Sam Houston State University, Huntsville, TX 77341, USA
Email: jzwang@shsu.edu
‡
National University of Defense Technology, Changsha, Hunan 410073, China
Email: hutingbo06@163.com
§
Huazhong University of Science and Technology, Wuhan 430074, China
Email: hongli@hust.edu.cn
Abstract—In this paper, a novel classification paradigm,
termed Spectral-Spatial One Dimensional Manifold Embedding
(SS1DME), is proposed for classification of hyperspectral imagery
(HSI). The proposed paradigm integrates the spectral affinity
and spatial information into a uniform metric framework. In
SS1DME, a spectral-spatial affinity metric is utilized to learn the
similarity of HSI pixels. Moreover, a pixel sorted based classifica-
tion scheme, called 1-Dimensional Manifold Embedding (1DME),
which is an extension of smooth ordering, is introduced for
objective classification. Four main steps are involved in SS1DME.
First, for a high dimensional data set, the proposed paradigm
employed the spectral-spatial affinity metric to calculate pixelwise
affinity. Next, we embed the whole data set into multiple 1-
dimensional manifolds so that connected point s have the shortest
distance. Then, using the spinning average technique and self-
learning scheme, a feasible confident set is constructed from
the unlabeled set, where data points in feasible confident set
are added to the labeled set in proportion. Finally, we use the
extended labeled set to learn the interpolated function, which
will lead to classification of unlabeled points. This approach is
experimentally superior to some traditional alternatives in terms
of classification performance indicators.
Index Terms—Feature extraction, 1-dimensional manifold em-
bedding, smooth ordering, pixel sorting, spectral-spatial infor-
mation, self-learning, hyperspectral image classification.
I. INTRODUCTION
During the last decades, the massive application of remotely
sensed hyperspectral techniques has promoted the develop-
ment of land-covers classification with high precision [1].
However, most traditional classification methods solely use
spectral information to learn the classifier. Consequently, the
classification results are proved to be unsatisfactory enough
[2]. To futher improve classification performance, recent in-
terest has metastasized to explore both spectral and spatial
information [3]. For example, in [4], J. Li employed active
learning before multinomial logistic regression (MLR) to
segment hyperspectral image. The model in [5] employed
composite kernel (CK) which intergrades both spectral and
spatial information into the support vector machine (SVM)
kernel. Another methods that aim at postprocessing the classi-
fication map provided a filtering alternatives according to the
spatial structure and classification confidence of HSI pixels.
For example, the method in [6] proposed an edge preserving
filtering to obtain the final classification map that is generated
by the state-of-the-art SVM classifier. Besides these methods,
many worldwide r esearchers have also proposed other methods
to combine the spatial information. For example, the authors in
[7] shows that the the class labels can be predicted by solving
a sparsity constrained optimization problem.
Recently, I. Ram et al. [8] developed the smooth ordering
technique. This method has shown to be highly effective in
image denoising [9], inpainting, as well as image deblurring
[10]. The core idea behind smooth ordering is based on the
fact that s mall patches with maximum overlaps are more likely
to be adjacent in a 1-dimensional sequence. Hence, a key step
in smooth ordering is the permutation operator. By finding the
shortest path that visits each patch once, these small patches
will become smooth in the 1-dimensional sequence so that the
1-dimensional signal processing tools (such as interpolation
and filtering) can be directly applied to the 1-dimensional
coefficients. A key assumption in smooth ordering is that
under a distance measurement, proximity between two patches
implies proximity between their properties.
In this paper, a novel algorithm, termed Spectral-Spatial
1-Dimensional Manifold Embedding (SS1DME) classification
algorithm is proposed for accurate spectral-spatial classifica-
tion of hyperspectral images. The proposed method i ntegrates
multiple 1-dimensional manifolds based on the smooth order-
ing principle. This is to ensure that the continuity of their
properties (such as spectral signature and class labels) could be
maintained in the reordering sequences. To tackle the problem
of limited sample size, we use the self-learning scheme,
which is commonly used in other classification methods, to
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2015 IEEE