IEEE Geoscience and Remote Sensing Magazine - June 2021 - 65

Hong et al. further extended their model to a deep version,
called JPLAY, with a k-layered linear regression:
PUi i=1
,{ }
s.t.
k
min 2
1
()
XX XYXx
MPXP
ii ii i$# (15)
==
-+ +
UU , ,, ,
() ({ })
iiiWX U k
2
F
-11 1
with PPW =
2
F
and
k
X({ }) tr()i i =1 = /
k
UUXLXU
XU UX
<
-1
-1
i =1
k
+-i 11i ii
i =1
/
<
2
-- F
.
gg !! 2 gg MM .
() W()
t+1
t
2
JPLAY attempts to open the black box of deep networks
in an explainable way using multilayered, linearized modeling.
With explicit mappings and physically meaningful
priors, the nonconvex JPLAY takes a big step toward an interpretable
AI model.
SEMISUPERVISED MODEL
Because the act of labeling samples is extremely expensive,
particularly for RS images covering a large geographic region,
the joint use of labeled and unlabeled information then becomes
crucial in DR and classification. A simple and feasible
strategy for semisupervised learning is to integrate supervised
and unsupervised techniques, e.g., LDA and locality
preserving projections [85]. By simultaneously constructing
graphs of labeled and unlabeled samples [e.g., using (12) and
(13), respectively], (9) be can easily extended to a semisupervised
version, leading to semisupervised discriminant analysis
(SSDA) [86]. Zhao et al. [87] further improved the SSDA
performance by using " soft " (or pseudo) labels predicted by
label propagation (LP) instead of directly using unsupervised
similarities among unlabeled samples. Similarly, Wu et al.
[88] generated pseudolabels using the Dirichlet process and
achieved a novel SSDA approach to learn low-dimensional
HS embedding. These methods are performed surrounding
various handcrafted graph structures (W).
Another idea is to simulate brain- or human-like behaviors
in the semisupervised DR task. It is well known that
the feedback reward is a key component that forms the intelligent
information processing system. Inspired by it, the
authors of [89] developed an iterative multitask learning
(IMR) framework by adaptively learning the LP on graphs
to simulate the feedback mechanism, thereby achieving the
HS DR process more effectively and efficiently. The IMR is
a semisupervised extension of (14) with graph learning,
which can be generally modeled as
min
s.t.
PU L,,
where Y1
UU IL
MPUY
j 1
2
/
=
< = ,,
!C
and Y2
ples from Y, respectively, W =
()
PP , and UUY
2
F
(16)
denote the labeled and unlabeled samX()
tr(=
JUNE 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
FIGURE 7. An example of clarifying the graph structure of the JPSA
method, where Wp
and Wsp
subgraphs and Wa
superpixels.
denote the pixel- and superpixelwise
is the aligned graph between the pixels and
65
jj ++
-
2
F
WX
() ()
PU
In addition, another intelligent feature-extraction algorithm,
named joint and progressive subspace analysis (JPSA),
which is extended from [84], was presented in [90] by attempts
to align pixels and superpixels for spatial-spectral
semisupervised HS DR. JPSA basically follows the JPLAY
framework, but the major difference is the graph structure
W. The graph in JPSA consists of not only pixel- and superpixelwise
similarities but also of aligned components between
pixels and superpixels. Figure 7 provides an example
to clarify the graph structure of JPSA. Note that the JPSA's
graph can be seen as a full data-driven structure, which
can, to a great extent, self-express the intrinsic properties of
HS data, further achieving intelligent information extraction
and DR.
EXPERIMENTAL STUDY
Classification is explored as a potential application to
evaluate the performance of SOTA DR algorithms, including
original spectral features (OSFs), OTVCA [63], [182],
RLMR [75], [183], FSDA [79], JPLAY [84], [184], IMR [89],
HS Pixels
HS Superpixels
1
Wp
Wa
0.9
0.8
0.7
0.4
0.5
0.6
Wa
Wsp
0.1
0.2
0.3
()
t
(17)
<
ii ii
2
=1
1
LY U ).<<
The nonconvex constraint C with respect to the
variable L can be summarized as
LL LL)
C {, ,,tr(},Lc:==
<
pq pq,, ! )00 =
pq pq,, = *
where c > 0 is a scaling constant. Equation (16) is a typical
data-driven graph-learning model that is capable of automatically
learning the graph structure from the data without
any handcrafted priors. By using an iterative strategy to
simulate the feedback system, M()t
+1
2
in the t + 1-step can
be updated by the graph-based LP on the learned graph of
the t-step W :()t
HS Superpixels
HS Pixels
IEEE Geoscience and Remote Sensing Magazine - June 2021

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