IEEE Geoscience and Remote Sensing Magazine - September 2021 - 81

A similar approach is presented in [174], which performs
sparse spectral clustering by using correntropy information.
For an HSI [, ,] ,
two arbitrary band images Ii
II II RN
and Ij
= 12 f !
Corre (, )( ,),
nI I M l
Ni,
vv=
=
j
1 / U II
1
M
li lj
where the Gaussian kernel () (/ ) and v is
U =-v
exp
zz 2
2
v
2
the bandwidth parameter [174].
In clustering-based BS methods, a statistical criterion,
such as MI [62], [69], [117], [122], [128], [168], [175]-[177]
or divergence [44], [100], [118], [178], [179], is used to measure
the similarity or dissimilarity between bands. Most
MI approaches constitute UBS methods, but the incorporation
of the GT was found to be effective for class discrimination
[176]. Traditional MI-based criteria commonly use
bivariate MI (BMI) to approximate the ideal MI-based criterion.
However, these BMI-based criteria generally miss
the bands that have discriminative information.
Several criteria based on band correlation [68], [103],
[146], [180], [181], band decorrelation [44], [69], [103],
[182], phase correlation [183], and spectral correlation
[66] are explored, where the main focus of the algorithms
is to remove redundancy among bands. Most of
the approaches use spectral information, such as spectral
shape similarity and dissimilarity [128], for BS, while,
with other approaches, spatial information is also exploited
for identifying the most relevant bands; these
include spatial invariant separability [78], spatial entropy-based
MI [93], and multidimensional local spatial autocorrelation
[140]. For finding the most distinct bands,
orthogonal subspace projection (OSP) [76], [184] and the
KLD [118] are considered by many researchers to operate
between two selected bands. It has been observed that
some key bands that are more informative and discriminant
than others may end up missing from the selected
subset. On the contrary, band ranking methods evaluate
the relevance of each feature independently, thus leaving
potentially redundant features. To overcome this issue, a
novel triangular factorization and ranking-based UBS
is introduced in [133] and found to be more effective
than the information divergence (ID), MVPCA, and MI
approaches in terms of computational complexity. Other
approaches, such as the information quality/gain [146],
[148], [185], stable zone unmixing [123], NMF [124], and
LP [105], [139], include some information-theoretic measures,
which results in less residual redundancy in the
BS process.
Other than the information-theoretic ones, measures
based on the extraction of spatial and/or spectral
features are exploited for BS [90], [186]. Various applications,
including endmember extraction and image quality
assessment, are explored in [73] and [187]-[190]; statistical
and wavelet data analysis is performed to extract
the feature set [191] and incorporated at a later stage for
SEPTEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
(8)
is given by
MN the correntropy for
#
feature-based BS. Such approaches are proposed for classification,
exploiting the spectral-spatial information of
an HSI [94]. A similar feature-based saliency-bands and
scale-selection method [86] calculates the trace tr(I) and
determinant det(I) of each HSI pixel, as defined in (9)
and (10):
tr () (),II I
=+
where ()Iii
TT TT
ii jj
tII IIii jj
TT TT TT
ij
(9)
de () () (( ))2,=- (10)
TT represents the two-order-difference results
for hyperspectral band image i. The variables defined in the
preceding possess a strong ability to detect the local structures
of an image.
A channel capacity-based criterion for band subset selection
(BSS) is presented in [192]. The original full-band
set is treated as a channel input space, and a selected-band
subset is similarly treated as a channel output space. Then,
BSS is carried out by Blahut's algorithm, which iteratively
finds the best possible input space, i.e., the one yielding
the maximal channel capacity. As a result, band prioritization
and interband decorrelation, which are generally required
by traditional BS approaches, are not needed here.
HYBRID APPROACH
Hybrid approaches can consist of an ensemble of direct, information-theoretic
correlation, divergence, and sparsity-enabled
measures. Sparsity-promoting iterated constrained
endmembers is an example hybrid approach in the context
of endmember detection [74], [193]. Various sparsityenabled
and hybrid approaches are discussed in [9]. However,
the volume of research articles that contain hybrid
approaches is limited, which suggests that further work
is needed. Since BS methods result in different subsets of
bands, each with its own merit, they also can be fused to
identify the most significant and redundant bands. Recently,
such a BS fusion method was proposed [194], merging
results obtained by various BS techniques. A further selection
strategy is based on the joint band subset, which assigns
a probability to each band; higher-priority bands are
collected as the band subset.
GROUPING AND RANKING STRATEGIES
A framework that organizes grouping and ranking strategies
is presented in Figure 8. Generally, clustering/ranking
and hybrid approaches can group data and place bands in
an ordered sequence, but they will not directly produce a
final band subset. To achieve the latter result, an additional
step called selection is needed, which is discussed later in
the article. Recently, such an adaptive subspace partition
strategy (ASPS) was presented in [195], where an HSI is partitioned
into multiple subspaces and the noise level of each
block is estimated with the help of variance information.
Further representative bands are selected using two different
approaches: 1) minimum noise and 2) distributing the
variance of each subcube.
81
IEEE Geoscience and Remote Sensing Magazine - September 2021

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