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Linear Versus Nonlinear PCA for the Classication of
Hyperspectral Data Based on the Extended
Morphological Proles
Giorgio Licciardi, Prashanth Reddy Marpu, Jocelyn Chanussot, Jon Atli
Benediktsson
To cite this version:
Giorgio Licciardi, Prashanth Reddy Marpu, Jocelyn Chanussot, Jon Atli Benediktsson. Linear Versus
Nonlinear PCA for the Classication of Hyperspectral Data Based on the Extended Morphological
Proles. IEEE Geoscience and Remote Sensing Letters, IEEE - Institute of Electrical and Electronics
Engineers, 2012, 9 (3), pp.447-451. �10.1109/LGRS.2011.2172185�. �hal-00797814�
LINEAR VERSUS NONLINEAR PCA FOR THE CLASSIFICATION OF
HYPERSPECTRAL DATA BASED ON THE EXTENDED MORPHOLOGICAL
PROFILES
Giorgio Licciardi
∗
, Prashanth Reddy Marpu
†
, Jocelyn Chanussot (IEEE Senior Member)
∗
, Jon Atli Benediktsson (IEEE Fellow)
†
∗
GIPSA-Lab. Grenoble Institute of Technology, Grenoble, France
†
Faculty of Electrical and Computer Engineering. University of Iceland, Reykjavik, Iceland
E-mail: Giorgio-Antonino.Licciardi@gipsa-lab.grenoble-inp.fr
Abstract—Morphological profiles have been proposed in
recent literature, as aiding tools to achieve better results for
classification of remotely sensed data. Morphological profiles
are in general built using features containing most of the in-
formation content of the data, such as the components derived
from principal component analysis (PCA). Recently, non-linear
PCA (NLPCA), performed by auto-associative neural network,
has emerged as a good unsupervised technique to fit the
information content of hyperspectral data into few components.
The aim of this paper is to investigate the classification
accuracies obtained using extended morphological profiles built
from the features of non-linear PCA. A comparison of the two
approaches has been validated on two different datasets having
different spatial and spectral resolution/coverage, over the
same ground truth, and also using two different classification
algorithms. The results show that the NLPCA permits to obtain
better classification accuracies than using linear PCA.
Keywords-Extended Morphological Profiles; Neural Net-
works; Nonlinear Principal Component Analysis; Classifica-
tion.
I. INTRODUCTION
Morphological profiles (MP), which combine spectral and
spatial information, have been shown to be effective tools for
classification of remote sensing data [1] [2] [3] [4] [5] [6].
An MP of a gray-level image (or a feature) can be defined
as a sequence generated with the morphological opening
by reconstruction and closing by reconstruction operations,
using structuring elements of increasing size. An extended
morphological profile (EMP) is constructed by stacking the
MPs built using different features.
Building EMP from the spectral bands of hyperspectral
images (HS) can be not convenient due to their huge number
of bands, so a reduction of the number of bands preserving
the information contents became important. It was suggested
in [4] to build the EMP from the top few components
obtained from the principal component analysis (PCA) trans-
formation which retain most of the variance of the image.
This approach was successfully applied in classification of
hyperspectral images, resulting in better accuracies com-
pared to simply using the spectral information only. Similar
approaches, using combinations of morphological operators
have been presented in literature [7] [3]. In particular it
has been observed that better classification accuracies can
be obtained using the nonlinear features from kernel PCA
(KPCA) instead of the features from PCA [8]. In both
cases, the derived components are ranked in terms of the
amount of variance. This means that the information content
is not equally distributed among the components, where
the first one is always more relevant than the others. The
dimensionality reduction using PCA or KPCA is achieved
by discarding the less relevant components. On the other
hand, Nonlinear Principal Component Analysis (NLPCA),
performed using Autoassociative Neural Networks (AANNs)
[9], produces a limited set of components in which the
information content tends to be uniformly distributed. The
purpose of this paper is to investigate the improvements
introduced by using EMP built from NLPCA and comparing
it with the results obtained with PCA and KPCA. The
paper is organized as follows. In sections II and III the
EMP and the NLPCA will be presented, respectively, while
a comparison of the classification results obtained using
EMP generated from NLPCA and PCA will be presented
in section IV. Finally, conclusions are drawn in Section V.
II. EXTENDED MORPHOLOGICAL PROFILE
In mathematical morphology, one of the most used ap-
proaches to analyze spatial inter-pixel dependency is the
morphological profile, which has been successfully used
to extract spatial information from high spatial resolution
images [1]. The idea at the base of the MP is to apply
geodesic closing/opening transformations of increasing size,
to build a certain set of opening profiles (OP) and closing
profiles (CP). The opening/closing profiles P at pixel x of
the image f are defined as a p-dimensional vectors:
P
i
(x) = γ
(i)
R
(x), ∀i ∈ [0, p] (1)
Where γ
(i)
R
can be the opening or closing by reconstruc-
tion with a structuring element (SE) of size i.
By grouping the OP, CP and the image f(x), the (2p+1)-
dimensional vector is the MP which is defined as:
MP (x) = [CP
p
(x), ..., f(x), ...OP
p
(x)]. (2)
It is clear from the representation of MP in 2 that applying
MPs directly to the hyperspectral data with huge number of
bands leads to a huge increase in the number of features.
The stacking of the q(2p+1) MPs obtained with different
features (where q is the number of retained components), is
called Extended Morphological Profile (EMP).
III. NONLINEAR PRINCIPAL COMPONENT ANALYSIS
One of the main difficulties in processing HS images
is related to the very high number of spectral bands.
Applying any processing technique to each band of the
HS image, can lead to a non acceptable increase of the
computational time of the entire process. Therefore, it is
generally desirable that a reduction in the number of features
is achieved without loosing the relevant spectral information
of the original dataset. In the literature, there exist many
methods for representing the information content in lower
dimensionality domain, called feature extraction techniques
[10]. Two of the most popular feature extraction methods
for data representation are Principal Component Analysis
(PCA), where a set of uncorrelated transformed features is
generated and the Independent Component Analysis (ICA),
where a computational method for separating a multivariate
signal into additive subcomponents supposing the mutual
statistical independence of the non-Gaussian source signals
[11]. For these techniques, the dimensionality reduction is
obtained by discarding the components with the lowest infor-
mation content. Also, as most of them are linear methods,
the resulting components are linearly uncorrelated but the
physical representation of the image may be lost. NLPCA,
originally introduced by Kramer [12], is based on a multi-
layer perceptron (MLP) commonly referred as (AANN) or as
autoencoder [13] [14]. The AANNs are conventional Neural
Networks (NNs) featuring feedforward connections and sig-
moidal nodal transfer functions, trained by backpropagation
algorithm. The particular network architecture used employs
three hidden layers, including an internal bottleneck layer of
smaller dimension than either input or output. The network
is trained to perform identity mapping, where the input has
to be equal to the output. Since there are fewer units in
the bottleneck layer compared to the output, the bottleneck
nodes must encode the information obtained from the inputs
for the subsequent layers to reconstruct the input. In such
a way, the nonlinear principal components (NLPCs) can
be extracted from the bottleneck nodes, after the training
of the AANN. The main task in designing the AANN
is the selection of the number of nodes minimizing the
information losses of the training.This problem was solved
by a grid search algorithm varying recursively the number
of nodes and evaluating the respective error. The topology
producing the lowest error was then selected. Compared to
linear reduction techniques, NLPCA has many advantages.
First of all, while linear methods can detect and discard
linear correlations among spectral bands, NLPCA detects
both linear and nonlinear correlations. Moreover, in NLPCA
the information content is equally distributed among the
components [15].
In this paper we propose the use of NLPCs to form base
images for the EMP. The NLPCs are obtained from an
AANN having sigmoidal activation function, trained with
Scaled Conjugated Gradient algorithm (SCG). Once trained
the AANN, the output of the bottleneck layer will be used
as NLPCs and the resulting EMP, will be used as input for
the classification task.
IV. EXPERIMENTS
In this section we present results of the proposed approach
applied to two different HS images having different spatial
and spectral resolution/coverage, over the same ground truth.
In both experiments we classified the EMP built from the
NLPCs extracted from a HyMap image and from a CHRIS
image. HyMap is an airborne 4 spectrometers sensor (VIS,
NIR, SWIR1 and SWIR2), providing 128 bands across
the reflective solar wavelength region of 0.45-2.5 µm with
contiguous spectral coverage (except in the atmospheric
water vapor bands) and bandwidths between 15-20 nm (Fig.
1-a). The CHRIS image was acquired in Mode 1 configu-
ration, having 62 spectral bands, with a spatial resolution
of 34 m at nadir and a spectral coverage of 0.45-1.03
µm (Fig. 1-b). Both images were acquired over the same
area during the ESA - SPectra bARrax Campaigns 2003
(SPARC) campaign (http://www.uv.es/leo/sparc/) carried out
in Barrax, La Mancha, Spain, from 12 to 14 of July 2003.
The Barrax area is mainly used for agricultural cultivations
and has been investigated for many years. It is characterized
by a flat morphology and large, uniform land-use units,
mainly composed by different agricultural types. During the
campaign an extensive ground truth was produced (Fig. 1-
c) and was used to build the ground truth in this study.
The reference classes used for the classification are: Corn,
Papaver, Potatoes, Alfalfa, Wheat, Barley, Garlic, Vineyards,
Bare soils, Onion and Barley stubbles, resulting in about
60.500 and 2.500 pixels for Hymap and Chris, respectively,
equally distributed between training and test sets. To eval-
uate the effectiveness of the method, the classification was
performed by two different algorithms i.e. neural networks
(NN) and support vector machines (SVM). A comparison
with the classification accuracies obtained using standard
PCA and kernel PCA with the EMP, shows the enhancement
introduced by the nonlinear principal component analysis. In
PCA and KPCA, the dimensionality reduction is performed
discarding the features less informative, but while in PCA
most of the information content is retained in the first few
features, KPCA requires more components. This means that
kernel PCA needs a large number of components, increasing
the dimensionality of the data, resulting in a huge number of
features when building morphological profiles. Moreover, in
KPCA, the choices of the kernel parameter and the sample
size to perform kernel PCA are very important and determine
these parameters is not an easy task. In particular, for both
images, KPCA was performed with 1500 samples, and the
kernel parameter was selected as twice the average distance
between all the pixels. A tuning of these parameters was
not performed because, being strongly dependent on the
randomly selected sample set, it will require a further pro-
cessing step, that cannot be compared with other approaches.
The comparison was carried out in terms of (OA) overall
accuracy ( ratio between the total number of correctly
classified samples and total number of test samples), K
Kappa coefficient of agreement (percentage of agreement
corrected by the amount of agreement that could be expected
due to chance alone), and the class accuracy (percentage of
correctly classified samples for a given class).
(a) Hymap
(b) Proba
(c) Ground truth
Figure 1. False color RGB of Hymap dataset (a) and CHRIS (b).
The map (c) shows the ground truth acquired during the ESA-
SPARC campaign.
A. Hymap dataset
The feature extraction from the HyMap image using
AANN was performed by a grid-search algorithm, varying
the number of nodes in the bottleneck and in the other two
hidden layers looking for the lowest Mean Square Error
(MSE). The optimal solution was found with 6 nodes in
the bottleneck layer, corresponding to 6 NLPCs and 55
nodes in the outer hidden layers. A circular SE with a step
size increment of 2 was used. Four openings and closings
were computed for each component, resulting in a EMP of
dimension 9X6 = 54. As for the PCA and KPCA, the EMPs
were constructed using the first components corresponding
to more than 99% of the cumulative variance, resulting
in 45 and 135 EMP, respectively. Analyzing the confusion
matrices in tables I-II and the classification maps in Fig.
2 it is evident that using NLPC to build EMP improves
the classification accuracy with both training algorithms.
Good accuracies were achieved in all classes except for
Alfalfa, that has good accuracy only using NN and NLPCA.
This problem raises from the small spectral differences
between Alfalfa and Potatoes cultivations that have not been
completely synthesized. KPCA reaches good accuracies for
all other classes except for Bare soil with SVM. This because
of the strong spectral similarity with Barley stubble.
Feature Raw P C A N LP CA KP CA
N. of features 126 5 6 15
N. of EMP 45 54 135
OA (%) 75.5792 74.1682 79.6533 73.1162
k 0.7252 0.7090 0.7654 0.6975
Corn 99.95 99.55 99.89 99.92
Papaver 100 99.52 100 100
Potatoes 96.12 99.21 99.98 100
Alfalfa 30.95 37.21 37.39 36.25
Wheat 99.28 95.02 99.29 99.96
Barley 100 99.66 99.74 99.57
Garlic 100 100 96.66 100
Vineyards 97.27 98.98 97.26 95.22
Bare soil 39.67 27.03 62.91 28.68
Barley stubbles 99.23 99.33 74.53 97.99
Onions 99.36 98.92 100 100
Table I
CLASSIFICATION RESULTS FOR THE HYMAP DATASET USING
SVM CLASSIFICATION ALGORITHM.
B. CHRIS dataset
Following the same procedures used in the previous
experiment, an AANN, having 4 nodes in the bottleneck
layer and 25 in the outer hidden layers, was used to extract
4 nonlinear principal components from the original 62 bands.
Also in this case a circular SE with a step size increment of
2 was used and four openings and closings were computed
for each component. The resulting dimensionality of EMP
was 9X4 = 36. The 99% of the cumulative variance of the
PCA was retained by the first 4 components, resulting in
a dimensionality of the EMP of 36 while KPCA needs 15
components, corresponding to 135 EMP. The results reported
in tables III-IV and in Fig. 3, show once again that the
best performances were obtained using NLPCs to build the
EMP for both NN and SVM classifications. Compared to the
HyMap experiments, it is evident that the highest accuracies
Feature Raw P CA NLP CA KP CA
N. of features 126 5 6 15
N. of EMP 45 54 135
OA (%) 79.6533 72.5309 81.9068 74.7217
k 0.7654 0.6912 0.7930 0.7147
Corn 99.89 99.55 99.73 99.48
Papaver 100 99.52 99.95 98.94
Potatoes 99.98 99.21 99.98 86.99
Alfalfa 37.39 37.51 75.15 27.06
Wheat 99.26 95.02 94.25 99.70
Barley 99.74 99.66 91.47 43.10
Garlic 96.66 100 99.64 99.64
Vineyards 99.81 98.98 99.18 93.29
Bare soil 39.67 27.03 79.14 82.27
Barley stubbles 99.33 68.76 75.57 99.97
Onions 100 98.92 98.66 97.96
Table II
CLASSIFICATION RESULTS FOR THE HYMAP DATASET USING A
NN CLASSIFICATION ALGORITHM.
Figure 2. Classification results obtained from the Hymap image
using SVM classification algorithm on EMPs built from PCA (a),
NLPCA (b) and KPCA (c), and using NN classification algorithm
on EMP built from PCA (d), NLPCA (e) and KPCA(f). The color
map is as follows:
Corn, Papaver, Potatoes, Alfalfa, Wheat, Barley,
Garlic, Vineyards, Bare soil, Barley stubble, Onions.
are obtained with the CHRIS data. Because the low spatial
resolution of the CHRIS data is more suited to the chosen
class types. The ground truth pixels in the CHRIS image
are related to the same land cover type and hence have
more uniform values than those from HyMap. This effect,
on the other hand, produced poor results in some cases. In
particular NLPCA and KPCA approaches show poor results
for the classification of Barley stubble class. This problem is
related to the classification algorithm and can be explained
analyzing the spectral signature of pixels of Barley stubble
class, that is very similar to the bare soil signature. This
leads alternatively SVM and NN to consider Barley stubble
as Bare soil.
Feature Raw P CA NLP CA KP CA
N. of features 62 4 4 15
N. of EMP 36 36 135
OA (%) 78.6342 73.8019 85.2636 70.0080
k 0.7513 0.6945 0.8277 0.6525
Corn 100 100 100 31.77
Papaver 100 100 100 100
Potatoes 100 100 100 99.17
Alfalfa 75.46 72.2 77.87 65.57
Wheat 100 100 100 100
Barley 100 100 40.00 100
Garlic 79.89 79.84 96.12 50.37
Vineyards 74.89 69.36 49.36 100
Bare soil 100 78.69 100 100
Barley stubbles 100 68.76 61.16 32.34
Onions 100 50.37 100 95.14
Table III
CLASSIFICATION RESULTS FOR THE CHRIS DATASET USING
SVM CLASSIFICATION ALGORITHM.
Feature Raw P CA NLP CA KP CA
N. of features 62 4 4 15
N. of EMP 36 36 135
OA (%) 89.1342 70.4872 93.3706 74.2259
k 0.8694 0.6647 0.9209 0.7094
Corn 100 100 100 99.89
Papaver 100 100 100 100.00
Potatoes 95.80 100 82.09 99.96
Alfalfa 74.74 32.62 100 37.39
Wheat 100 100 99.34 98.87
Barley 100 38.57 61.43 99.74
Garlic 100 100 92.25 96.66
Vineyards 86.19 46.38 94.86 99.55
Bare soil 83.72 100 100 39.67
Barley stubbles 100 76.86 26.45 74.53
Onions 100 50.37 99.26 100
Table IV
CLASSIFICATION RESULTS FOR THE CHRIS DATASET USING A
NEURAL NETWORK CLASSIFIC ATION ALGORITHM.
V. CONCLUSIONS
This paper presented a novel classification approach with
two main issues: a feature extraction method based on
NLPCA as a tool which is able to maintain the informa-
tion content of hyperspectral remote sensing imagery into
few components, and the construction of EMP with the
NLPCs, to include spatial information in the classification
task. Comparisons in terms of classification accuracies with
standard PCA and KPCA approaches, using a SVM and
a NN classifiers, demonstrates that NLPCA extracts more
informative features and does not suffer from the noise
contained in the HS data. The poor results obtained by
KPCA can be explained by the fact that the sample size may
not be enough, and also by the fact that kernel PCs are more
influenced by noise than the other components. Moreover
kernel PCA results in a large number of features, thus
increasing the dimensionality of the data, which increases
many times when building morphological profiles, allowing
