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RemoteSensingCorpus

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samples of the target domain. In this case, the data distributions remain unchanged, and the classifier is
adapted to the target data distribution using strategies
based on semisupervised learning. ◗The adaptation of the classifier by active learning (AL): This adaptation is performed by providing a lim -
ited amount of well-chosen labeled samples from the target domain. This is a special case of the previous fam -
ily, where we allow some new labeled examples to be
sampled in the target domain to retrain the model itera -
tively. Due to their acquisition cost, these samples need
to be selected well, according to their potential to lead
the model toward the desired target classifier.
The rest of this section details recent advances in these
four families. We will limit the discussion to approaches
specific to the remote sensing literature and invite the in -
terested reader to consult the specialized machine-learning
and computer vision literature in [ 13], [14], and [16 ].
SELECTING INVARIANT FEATURESThe first family of DA methods is based on the selec -
tion of invariant features that are usually a subset of the original set of features that are the most robust in
the face of changes from the source to the target do -
main. The main idea of the approach is to select features to reduce the difference between
(, ) PX Ys and (, ). PX Yt An
alternative strategy for encoding the invariance is based on
the inclusion of additional synthetic labeled samples in
the training set, a procedure known in machine learning
as data augmentation . A meth -
od adopting this strategy was
studied in [ 29], where sam -
ple-selection bias problems are addressed by enriching the training set with artificial
examples that correspond to
physically consistent varia -
tions of the training samples
(e.g., illumination, size, and
rotation). To limit the num -
ber of additional examples to be used by the support vector
machine (SVM), variations are generated only for the train -
ing samples considered as support vectors by the classifier
trained on the source domain only.
Let us consider the first strategy and focus on the analy-
sis of hyperspectral images as an application of particular interest. Hyperspectral sensors are capable of capturing
hundreds of narrow spectral bands from a wide range of
the electromagnetic spectrum, which is why they are par -
ticularly sensitive to subtle changes in image-acquisition
conditions, leading to a nonstationary behavior of the spec -
tral signature of the classes and, therefore, to problems that
should be solved by transfer learning and DA approaches.
Figure 4 shows an example of a shift in the signature of a
hyperspectral image acquired by the Hyperion sensor over
two areas of the Okavango Delta in Botswana.
In [30], the authors propose an approach for selecting
subsets of features that are both discriminative of the land-cover classes and invariant between the source and the target tHe coVaRiate SH iFt iS
a pa RticuLaR ca Se oF
Samp Le SeLection BiaS
wHe Re tHe BiaS DepenDS
onLY on t He input
VaRiaBL e X (anD not
on y).
Authorized licensed use limited to: ASU Library. Downloaded on March 08,2024 at 03:13:37 UTC from IEEE Xplore. Restrictions apply.
ieee Geoscience and remote sensin G ma Gazine june 201646
domain. The main idea of this
approach is to explicitly con -
sider two distinct terms in the criterion function for evaluat -
ing both the discrimination
capability
D of the feature
subset and the data set shift
P of the features between the
source and target domain. The first term is standard in filter
methods for feature selection and provides high scores when
the features selected show
some kind of dependency with the desired output (e.g., the
classes to be predicted). The
second term has been introduced to evaluate the invariance
of the feature subset between the two domains. The subset of
features
F is selected by jointly optimizing the two terms D
and ,P i.e., by solving the following multiobjective optimiza -
tion problem:
(( ),()), argmin FP F
||FlD-
= (1)where l is the size of the feature subset. Both D and P
are treated as functions of the subset of considered fea -
tures .F The specific definitions of the terms D and P
are reported in [ 30], considering their parametric esti -
mation (assuming Gaussian distribution of the classes)
in both the supervised and semisupervised DA settings. In [31], the two terms are defined considering kernel-
based dependence estimators and kernel embedding of conditional distributions, resulting in a nonparamet -
ric approach that does not require the estimation of the
class distributions as an intermediate step. Equation (1)
is solved by adopting a genetic multiobjective optimiza -
tion algorithm. The solution results in features with high
capability to discriminate classes (with a small value of
)D- and high stability on the two domains (with a small
data set shift ).P Adopting a multiobjective optimization
approach instead of considering a linear combination of
the two terms frees the user from specifying in advance
the relative importance of the two terms D and .P The
solution of the multiobjective problem allows one to find the solutions that represent the best tradeoffs of discrimi -
native and stable feature subsets for the specific transfer-
learning problem at hand.0 50 100 15001,0002,0003,0004,0005,0006,0007,000
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