IEEE Geoscience and Remote Sensing Magazine - June 2016 - 44

Source Domain
7,000
Class 1
Class 2
Class 3
Class 4
Class 5
Class 6
Class 7

6,000
5,000
4,000
3,000

Class 8
Class 9
Class 10
Class 11
Class 12
Class 13
Class 14

2,000
1,000
0

(b)

100

150

Target Domain

7,000

Class 1
Class 2
Class 3
Class 4
Class 5
Class 6
Class 7

6,000
5,000
4,000
3,000

Class 8
Class 9
Class 10
Class 11
Class 12
Class 13
Class 14

2,000
1,000
0

(a)

100

150

(c)

FiguRe 4. (a) A false color composition of a portion of the hyperspectral data set. (b) The mean spectral signature of the classes on the

source domain. (c) The mean spectral signature of the classes on the target domain.
domain. The main idea of this
approach is to explicitly conin tHe Remote SenSing
sider two distinct terms in the
LiteRatuRe, SeVeRaL
criterion function for evaluattecHniQueS HaVe Been
ing both the discrimination
pReSenteD to SoLVe tHe
capability D of the feature
subset
and the data set shift
tRanSFeR-LeaRning
P of the features between the
pRoBLem iRReSpectiVe
source
and target domain. The
oF tHe cauSe oF tHe Data
first term is standard in filter
Set SHiFt Between
methods for feature selection
SouRce anD taRget
and provides high scores when
DomainS.
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 optimization problem:
argmin (- D (F), P (F)),
|F|= l

(1)

where l is the size of the feature subset. Both D and P
are treated as functions of the subset of considered features F. The specific definitions of the terms D and P
are reported in [30], considering their parametric estimation (assuming Gaussian distribution of the classes)
in both the supervised and semisupervised DA settings.
In [31], the two terms are defined considering kernelbased dependence estimators and kernel embedding of
conditional distributions, resulting in a nonparametric approach that does not require the estimation of the
class distributions as an intermediate step. Equation (1)
is solved by adopting a genetic multiobjective optimization 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 discriminative and stable feature subsets for the specific transferlearning problem at hand.
ieee Geoscience and remote sensing magazine

june 2016

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