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acquisitions, in which the spectra are spatially detrended
using Gaussian processes to avoid shifts related to local -
ized class variability. In [ 49], the authors perform anom -
aly detection by a sparse discriminative transform that maximizes the distance between the anomaly class and
the background classes (defined as a set of endmembers)
and minimizes the distance between the source and target distributions after reduction by PCA. In [ 50], the authors
consider the domains as multidimensional graphs and propose to align the domains by solving a graph-matching problem. Finally, the authors in [ 51] find a multispectral
mapping between source and target spectra to project the labeled pixels of the source domain into the target domain. Tie points are found between the labeled source pixels and
the pixels in the target by registration, and then the map -
ping between the source and target is learned by regression
between the corresponding pairs. Then the labeled pixels
are projected into the target domain and are used to train
a classifier therein. As for [ 40], partial overlap between the
images is required.
As one can see in Table 1 , some methods will be more
suitable than others, depending on the problem. For exam -
ple, canonical correlation-based methods can be used only
for coregistered data, while nonmultiview methods such as
KPCA and (semisupervised) transfer component analysis [(SS)TCA] cannot align more than two domains at a time.
In the following, we compare a series of methods on
the challenging problem of transferring a classifier over a multiangular sequence of images over Rio de Janeiro [ 52],
illustrated in Figure 6 . More details on this example can be
found in [ 38]. The images are not coregistered but are all
acquired from a single pass of the WorldView2 sensor. For
this reason, the only shifts observed are due to angular ef -
fects. The problem is an 11-classes problem, and a separate
ground truth is provided per each image ( Table 2 ).
The adaptation experiment is designed by taking the
nadir image (off-nadir angle
.)609 i=% as the source im -
age and using all the others as target images. We apply
the PCA, KPCA, graph matching (GM), and semisuper -
vised manifold alignment (SSMA) transforms and then
train a classifier using 100 labeled pixels from the source domain and predict all of the target domains using that
classifier, without further modifications. For PCA, KPCA, and GM, the adaptation is done for each target domain separately, while, for SSMA, a single adaptation projec -
tion is obtained for all domains at once. For SSMA, we
also used 50 labeled pixels per class from each target do -
main. To be fair in the evaluation, the projections for the
PCA, KPCA, and GM methods are obtained in an un -
supervised way, but then the classifier is trained using the original training points from the nadir acquisition, stacked to the transformed labeled pixels of the domain
to be tested. We also add a best-case scenario, where we
directly use labeled samples from the target domains for the classification. The results are illustrated in Figure 7 .
The prediction in the off-nadir images using the origi -
nal training samples from the nadir image leads to poor results, especially for strong off-nadir angles. All of the
methods considered leverage the decrease in performance
and lead to a quasi-flat prediction surface (meaning that the model can predict correctly, regardless of the angu -
lar configuration) with particularly good performance by the SSMA method, which seems to best align the data TABLE 2. Th E NUmBER Of LABELED PIxELS AVAILABLE fOR
EACh DATA SET IN Th E mULTIANgULAR ExPERI mENTS
(i = Off-NADIR ANgLE).
CLASS i38.79-%29.16-%6.09%26.76%39.5%
Water 83,260 79,937 66,084 63,492 54,769
Grass 8,127 8,127 8,127 8,127 8,127
Pools 244 244 223 195 195
trees 4,231 4,074 3,066 3,046 3,046
concrete 707 719 719 719 696
Bare soil 790 790 790 790 811
asphalt 2,949 2,949 2,949 2,827 2,827
Gray
buildings 6,291 6,061 5,936 4,375 4,527
red
buildings 1,147 1,080 1,070 1,046 1,042
White buildings 1,683 1,683 1,571 1,571 1,571
shadows 1,829 1,056 705 512 525
tarmac 5,179 5,179 5,179 2,166 2,758
−38.79° −29.16° 6.09° 26.76° 39.5°
Figu Re 6. The five images of the Rio de Janeiro angular sequence [52].
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ieee Geoscience and remote sensin G ma Gazine june 201650
distributions. This is not surprising, since, among the test -
ed methods, SSMA is the only one with a clear discrimina -
tive component that uses labels in all domains to define
the projections.
ADAPTING CLASSIFIERS WITH
SEMISUPERVISED APPROACHES
A widely used approach to DA is based on adaptation of
the model of the classifier derived on the source domain
to the target domain. In the literature, the approach is de -
fined as semisupervised if this adaptation is based only on
unlabeled samples of the target domain (no target train -
ing samples are used). The rationale of semisupervised ad -
aptation is to use the relations between the distributions of the source and target domains to infer a reliable solu -
tion to the problem described in the target domain. The
common assumption of most of the methods is that the
source and target domains share the same set of classes
and features.
The first attempts to address semisupervised DA in re -
mote sensing image classification were presented in [ 53],
where a DA technique is proposed that updates the parame -
ters of an already trained parametric maximum-likelihood
(ML) classifier on the basis of the distribution of a new im -
age for which no labeled samples are available. In [ 54], the
ML-based DA technique is extended to the framework of the Bayesian rule for cascade classification (i.e., the classifi -
cation process is performed by jointly considering informa -
tion contained in the source and the target domains). The basic idea in both methods is modeling the observed spaces
by a mixture of distributions, whose components can be es -
timated by the use of unlabeled target data. This is achieved by using the expectation maximization (EM) algorithm with the finite Gaussian mixture model. In [ 55] and [56 ],
DA approaches based on multiple-classifier and multiple-cascade–classifier architectures were defined. Gaussian ML classifiers, radial basis function neural networks, and
hybrid cascade classifiers are used as base classifiers. The