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matching algorithms that exploit the geometrical structure of the data. |
Problems related to DA are the sample selection bias |
and covariate shift [ 23]–[25 ]. The sample selection bias |
originates when the available training samples are not in - |
dependently and randomly selected from the underlying distribution (i.e., the training set is not a random sample of the population). This situation is very likely to occur in |
remote sensing problems where training points are usually |
selected and labeled through photointerpretation or field surveys. The covariate shift is a particular case of sample se - |
lection bias where the bias depends only on the input vari - |
able |
X (and not on .)Y Different operational conditions |
that result in biased training samples are discussed in [ 26]. |
Clearly, a training set xx{( ,),, (, )} Ty ynn 11f = obtained un - |
der a sample selection bias leads to skewed estimation of |
the true underlying distribution of the classes, resulting in an estimated |
(, )( ,) . PXYP XY! t For this reason, the effect |
of a sample selection bias is similar to the DA problem de - |
scribed previously. The covariate shift problem is generally not as severe as the general sample selection bias and the |
DA problem. Let us consider that both training sets on the |
source and target are samples with bias (a bias depending on X only, i.e., covariate shift) from the same joint distribution. |
The joint probabilities on the two domains can be factorized |
as |
(, )( )( |) PX YP XP YXss s= and (, )( )( |) . PX YP XP YXtt t= |
In this particular case of covariate shift, the estimated con - |
ditional probabilities will be approximately equal, while |
the marginal distributions will generally be different, i.e., |
(| )( |) PY XP YXst. tt and () () . PX PXst!tt |
Figure 3 illustrates the two different issues of DA |
and the sample selection bias with two explanatory ex - |
amples. The plots report the distributions of the labeled |
samples from two domains in a bidimensional feature space. A four-class classification problem is considered. |
In the case of DA, the class-conditional densities may |
change from the source to the target domain, possibly resulting in a significantly different classification prob - |
lem. Note that the distribution of the classes in the target domain may overlap with different classes on the source domain (see the green circle in the target domain that |
represents the location of the green class in the source). |
In this situation, training samples of the source domain |
can be misleading for the classification of the target |
domain [ 27], [28 ]. In the case of sample selection bias, Source Domain |
DA |
Sample |
Selection BiasTarget Domain |
FiguRe 3. Explanatory examples of DA and sample selection bias |
problems. The plots represent labeled samples in a bidimensional feature space on the source and target domain. A four-class |
classification problem is considered. In the case of DA, the class- |
conditional densities may vary from the source domain to the target |
domain, resulting in a significantly different classification problem |
(the green circles correspond to the location of the green classes in the source domain). In the case of sample selection bias, the |
aforementioned issue will not occur, resulting in a milder type of shift |
from the source domain. |
tHe Samp Le SeLection |
BiaS o Riginate S wHen |
tHe aVaiLaBLe tRaining |
Samp LeS aRe not |
inDepen DentLY an D |
RanDomLY S eLecte D |
FRom tHe unDeRLYing |
DiStRiBution . |
Authorized licensed use limited to: ASU Library. Downloaded on March 08,2024 at 03:13:37 UTC from IEEE Xplore. Restrictions apply. |
june 2016 ieee Geoscience and remote sensin G ma Gazine 45 |
source- and target-domain samples are drawn (with bias) |
from the same underlying distribution, generally resulting |
in a milder type of shift with respect to DA. (The problem |
of cross-domain class overlap is not likely to occur in sam - |
ple selection bias problems.) |
In real remote sensing problems, it is expected that the |
two aforementioned issues may occur at the same time and can be profoundly entangled, meaning that 1) the two |
theoretical underlying distributions |
(, ) PX Ys and (, ) PX Yt |
associated with the source and target domains, respec - |
tively, may differ because of changes in the image acquisi - |
tion conditions (e.g., radiometric conditions), and 2) the |
available training samples could be not fully representative |
of the statistical populations in their respective domains |
and will, therefore, lead to biased estimations of the class probabilities and to inaccurate classification models. In |
the remote sensing literature, several techniques have been |
presented to solve the transfer-learning problem irrespec - |
tive of the cause of the data set shift between source and |
target domains. The next section will present the different |
families of techniques that have been proposed in remote sensing image processing. |
a taXonom Y oF aDaptation met HoDS |
Adapting a model trained on one image to another (or a |
series of new images) can be performed in different ways. |
In this section, we detail recent approaches proposed in the remote sensing literature by grouping them into the |
following four categories: |
◗The selection of invariant features: A set of the input |
features (i.e., the original bands or additional features |
extracted from the remote sensing image) that are not |
affected by shifting factors are identified and selected before training the classification algorithm. According - |
ly, the features affected by the most severe data set shift are removed, and the classifier considers a feature space showing higher stability across domains. An alternative |
approach is to encode invariance by including additional |
synthetic labeled samples in the training set to extract features that better model the intraclass variability across |
the domains. |
◗The adaptation of the data distributions: The data |
distributions of the target and source domains are made as similar as possible to keep the classifier un - |
changed. With respect to the previous family, these |
methods work on the original input spaces and try |
to extract a common space where all domains can be |
treated equally. This is generally achieved by means of joint feature extraction. |
◗The adaptation of the classifier: Here, the classifica - |
tion model defined by training on the source domain is |
adapted to the target domain by considering unlabeled |
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