IEEE Geoscience and Remote Sensing Magazine - March 2017 - 46

TaBLE 2. cLaSSIFIcaTION PErFOrmaNcES IN ThE PErcENTaGE OF accUracY OBTaINED BY ThE DIFFErENT mEThODS
ON a hYPErSPEcTraL ImaGE.
DaTa SETS

NUmBEr OF
TEST SamPLES

NUmBEr OF
TraINING SamPLES

SVms, % [17]

Fcm-SVms, % [147]

SF-TSVms, % [126]

acTIVE SVms, % [59]

salinas-a corrected

3,569

400

81.34

83.24

82.60

84.11

800

82.94

83.64

84.48

85.20

1,200

83.47

84.45

85.20

85.79

likelihood. The exterior-class pixels are ignored, while the
pixels in the boundary region, including the misclassified
pixels, are classified again on a basis of the fuzzy-topology
connectivity theory. Experimental results demonstrate that
the FTSVM method outperforms standard SVMs, MLCs,
and fuzzy-topology-integrated MLCs.
HYPERSPECTRAL IMAGE CLASSIFICATION
To demonstrate the effectiveness of the representative techniques of each group in Table 1, we have compared standard SVMs [17] with active SVMs [59], [126] SF-TSVMs,
and FCM-SVMs [147]. The RBF kernel is used for all of
the SVM-based methods. The hyperspectral image used
in our experiment is the Salinas-A scene (Salinas-A corrected), which contains 86 × 83 pixels (i.e., 7,138 pixels),
204 bands, and six classes. The image is available at http://
www.ehu.eus/ccwintco/index.php?title=Hyperspectral_
Remote_Sensing_Scenes. For the purpose of investigation, the whole data set is
first sampled using a random
procedure and equally parS3VMs CAN IMpROVE
titioned into two subsets.
pERfORMANCE COMpAREd
From the first subset, which
TO STANdARd SVMs If THE
contains 3,569 pixels, three
training subsets of 400, 800,
uNdERLYING pRObLEM IS
and 1,200 points were crepROpERLY AddRESSEd
ated, while an unlabeled subANd THE CLuSTER
set of 2,369 pixels (i.e., 3,569
ASSuMpTION HOLdS.
- 1,200 = 2,369 pixels) were
generated. The most informative pixels were queried from
this unlabeled data, labeled, and then added to the training subset at each iteration as prescribed by the algorithms.
The second subset containing 3,569 pixels is used as the
test set. Note that the test set is used for neither training nor
model generation. Table 2 shows the performance of the
different representative methods in terms of the percentage of accuracy for three different training subsets. It can
be seen from the table that active SVMs obtained the best
accuracy in all experiments. The reason behind the good
performance of active SVMs is that the supervisor (human
expert) has correctly labeled the most uncertain pixels. It is
interesting to observe that the SF-TSVMs and active SVMs
yield comparable accuracy using the training subsets of
800 and 1,200 points.
46

CONCLuSION
In this review article, we have provided a quick reference
of the compendium of recently developed SVM-based techniques in RS applications. We also pointed out traditional
methods used for image classification. Most of the findings indicate that there is sufficient empirical evidence to
support the adoption of these processing algorithms. For
instance, the experimental results of the representative
techniques in Table 2 provide a snapshot of why the RS
community is interested in these advanced techniques for
image analysis. SVM-based strategies such as S3VMs and
active SVMs offer additional benefits in contrast to other
advanced classification models because they inherit the appealing properties of SVMs.
S3VMs can improve performance compared to standard
SVMs if the underlying problem is properly addressed and
the cluster assumption holds. If the training examples represent the actual distribution of the entire problem space,
S3VMs can enhance the accuracy compared to SVMs. Another critical assumption is that the initial training samples pose a bias on the part of feature space when looking for low density. Therefore, S3VMs should be designed
after cautious evaluation of the properties of the underlying problem when the training samples are incomplete
and moderately biased. The main problem of S3VMs is the
exponential computational complexity, because a large
matrix consisting of labeled and unlabeled samples must
be computed. A recent development of the convex optimization theory is the semidefinite programming problem,
which can be optimized in polynomial time. However,
the algorithm complexity appears too large to tackle largescale problems.
On the other hand, active SVMs can be an alternative
way to address problems that do not comply with cluster
assumption. This is particularly useful for VHR images that
have several millions of pixels because SVMs are computationally effective. Selecting batches of training samples
instead of a single one further reduces computational time.
However, they are essentially greedy strategies as the selection of a new point or a set of new points is influenced by
the current hyperplane.
Combined SVMs have been experimentally shown to
work under certain constraints, such as linearity, balanced
data set, and near Gaussian-distributed data. It is worth
noting that when more groups are introduced in modeling
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