IEEE Geoscience and Remote Sensing Magazine - December 2021 - 50

based SSC methods were developed for HSIs. A typical example
is the mass center-reweighted object-oriented SSC
(MCR-OOSSC) algorithm [135]. It flexibly models spatial
neighborhoods with various shapes via objects obtained
from oversegmentation and extracts more representative
and discriminative object mass centers as features to construct
the object sparse representation model, as in (17):
min +-m uuuuCY YC F subjectto diag^h 0
2
u
C
Here, Y RD#G
GG#
CTu 11.
u !
=
u
C R!
1
2
C = ,
(17)
is the object mass center data matrix and
is the associated sparse coefficient matrix, with G
denoting the number of objects. Based on the MCR-OOSSC
approach, in [136], a higher-order superpixel-based SSC algorithm
with a conditional random field (SP-SSC-CRF) was
proposed. It integrates the advantages of the SC4
and OOSSC
methods to generate an enhanced model and utilizes the conditional
random field to further smooth the within-class noise.
In general, these object/superpixel-based methods improve the
clustering performance to a certain degree and greatly reduce
the time cost by converting pixel clustering to object clustering,
which significantly increases the attractiveness of subspace
clustering in practical applications.
Moreover, to better evaluate the discriminative information
and more accurately learn the nonlinear structure of
HSIs, a Laplacian-regularized deep subspace clustering (LRDSC)
algorithm was proposed [137]. It combines subspace
clustering with the deep convolutional autoencoder network
to learn the nonlinearity of HSIs and extracts spectral-spatial
information through 3D convolutions and deconvolutions
with skip connections to fully exploit multilevel features.
Consequently, LRDSC obtains highly competitive clustering
performance for HSIs.
MULTIVIEW SUBSPACE CLUSTERING
Multiview subspace clustering methods take full advantage
of complementary information found in different domains
of HSIs to further improve the clustering performance. Generally,
each view corresponds to a specific feature domain,
such as the spectral feature domain, the contexture feature domain,
the shape feature domain, and so on. Such techniques
generally construct a unified model to integrate multiview
feature self-representation problems. A typical example is
the spectral-spatial-based multiview low-rank SSC (SSMLC)
method [138], which has been applied to HSIs [139]. Specifically,
it generates the spectral view by spectral partitioning to
obtain correlated bands and creates the spatial view by morphological
processing. In addition, another view is generated
by PCA to remove the serious noise in HSIs. By integrating
different views within the SSC framework, SSMLC can be
modeled as in (18):
m
CC,
12 Cm
,,
f
min / ii
i=1
)
,
^ CC CC F
1## !
subjectto YYCC 0,
ii ii
12 1
bb c++ -
==
h
diag^
50
h
/
ij mi j
,,
(18)
ij 2
C
min HK K
diag
^
subjectto
CY YC
C
h ^^
h
+-m
=
0 ,
2 hh
^
F
2
(19)
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2021
where m denotes the number of views and Yi
feature matrix of the ith view, with Ci
indicates the
representing the asso2
,
ciated coefficient matrix. The terms b1 , b and c are three
regularization parameters. The second term is utilized to
force the coefficient matrixes learned from different views
to share the same pattern. Through multiview learning,
the complementary information of HSIs can be effectively
integrated, and the discriminability of the representation
coefficients can be enhanced to some degree, which leads
to more accurate clustering results.
Considering the nonlinearity of HSIs, the SSMLC model
was extended to a kernel version, i.e., k-SSMLC [140]. It further
improves the clustering accuracy by introducing the kernel
technique to address the nonlinearly separable problem
of HSIs in the multiview subspace clustering framework. In
addition, to overcome the large computational burden of
multiview subspace clustering, a parallel SSMLC (p-SSMLC)
method was put forward [141]. It adopts a simple parallel
strategy to reduce the time cost of SSMLC. Specifically, given
the large size of remote sensing images, the HSI is first partitioned
into many nonoverlapping 3D blocks. Then, the
SSMLC method is applied to each 3D block to obtain the local
clustering results. Last, by merging these local clustering
outcomes, the final clustering result is obtained. By employing
the advanced parallel computing technique, the overall
time cost is significantly reduced, which further improves the
practicability of the computationally expensive multiview
subspace clustering models.
KERNEL SUBSPACE CLUSTERING
Due to the complex imaging environment and serious
interference from various nonlinear factors in the imaging
process, HSIs generally have an obvious nonlinear
structure, and different classes are generally not linearly
separable. However, most subspace clustering methods are
based on the linear subspace assumption, which utilizes
the union of linear subspaces to approximate the complex
nonlinear internal structure of HSIs, leading to a large systematic
error and poor separability among different classes.
IEEE Geoscience and Remote Sensing Magazine - December 2021

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