An Optimization-Based Ensemble EMD for
Classification of Hyperspectral Images
Yi Shen Member, IEEE, Zhi He*, Xiaoshuai Li, Qiang Wang Member, IEEE, Miao Zhang and Yan Wang
School of Astronautics, Harbin Institute of Technology, Harbin, P. R. China
Email: hzhdhz@126.com
Abstract—Extraction of the essential features from massive
bands is a key issue in hyperspectral images classification. Plenty
of feature extraction techniques can be found in the literature but
most of these methods rely on the linear/stationary assumptions.
The aim of this paper is to propose an alternative methodology
based on the ensemble empirical mode decomposition (EEMD)
and utilize the versatile support vector machine (SVM) as a
classifier. An optimization problem, which minimizes a smooth
function subjected to inequality constraints associated with the
extrema, is formulated in each iteration step to enhance the
benefits of the EEMD. Additionally, the intrinsic mode functions
(IMFs) extracted by the optimization-based EEMD are taken as
features of the hyperspectral dataset and classified by the SVM.
Simulations on the Washington D.C. mall hyperspectral dataset
confirm the promising performance of our approach.
Index Terms—hyperspectral images; ensemble empirical mode
decomposition (EEMD); classification; support vector machine
(SVM)
I. INTRODUCTION
Hyperspectral imaging has attracted much attention in re-
cent decades due to its sufficient object information and high
spectral resolution. One of the key issues in the hyperspec-
tral community is classification, in which the detection of
essential features from enormous bands and the selection
of classifiers for high classification accuracy are two crucial
issues. Basically, the former is achieved by feature selection
or extraction while the latter is associated with numerous
classifiers. Regarding the feature selection, Paskaleva et al
proposed a canonical correlation-based algorithm appropriated
for noisy and overlapping bands [1], while the immune clonal
strategy was applied to select effective bands according to
Yin et al [2]. Chen et al developed a graph-based feature
selection method for very high resolution imagery [3], and
Bruzzone et al selected the subsets of features with both
high discrimination ability and high spatial invariance [4].
Moreover, the original hyperspectral dataset is transformed
into other forms in terms of the feature extraction including
principal component analysis (PCA) [5], independent compo-
nent analysis (ICA) [6], discrete wavelet transform (DFT) [7],
empirical mode decomposition (EMD) [8], nonnegative matrix
factorization (NMF) [9], local discriminant analysis (LDA)
[10]. On the other hand, much work has also been carried out
to develop the classifiers. For instance, the k-nearest neighbor
(k-NN) classifier [11], artificial neural network (ANN) [12],
maximum likelihood (ML) classifier [13], decision tree (DT)
[14], markov random fields (MRF) [15], as well as the support
vector machine (SVM) [16]. Particularly, it is notable that
the SVM has provided competitive performance with other
classification methods and adopted to identify the categories
of various pixels in this paper.
To cope with the detection of essential features from mas-
sive hyperspectral images, an adaptive and data-driven tech-
nique inspired by the ensemble empirical mode decomposition
(EEMD) is addressed in this paper [17], [18], [19]. In greater
detail, the EEMD, which is achieved by sifting an ensemble
of white noise-added signal and taking the mean as final
decomposition results, can enhance the robustness of the EMD
[20] and alleviate some typical problems of the EMD including
the annoying mode mixing. Other than the above-mentioned
feature selection or extraction methods, the EEMD is not
subject to the linear/stationary assumptions and decomposes
the given spectral signal into several intrinsic mode functions
(IMFs) adaptively. In addition, it is worthwhile to note that
in each iteration step of the EEMD, the noise-added signal is
actually decomposed by the EMD, whose upper (or lower)
envelopes are generated by spline interpolation and suffers
from the undesirable over-/undershooting. To overcome these
drawbacks, the upper and lower envelops are directly calculat-
ed by formulating an optimization problem, which minimizes a
smooth function subjected to inequality constraints associated
with extrema of the signal, in each iteration step of the
EEMD [21]. As a consequence, the IMFs extracted by the
optimization-based EEDM are treated as new features of the
original hyperspectral dataset and selected as training samples
and testing samples of the SVM.
The outline of this paper is organized as follows. In Section
II, we introduce the existing EEMD and its modified version
motivated by the optimization problems. Section III provides
a brief description of the SVM, whereas the proposed hy-
perspectral classification method is stated in Section IV. The
simulation results are discussed in Section V to confirm the
effectiveness of the proposed method. Finally, the conclusions
are drawn in Section VI.
II. ENSEMBLE EMPIRICAL MODE DECOMPOSITION
The EMD is an adaptive time-frequency technique that
decomposes a time domain signal, in light of a process
called the sifting algorithm, into a complete and finite set
of data-driven basis functions termed as IMFs [20], [22],
[23]. It has been proved a powerful tool for extracting in-
trinsic components from non-linear/non-stationary signal and