IEEE Geoscience and Remote Sensing Magazine - September 2021 - 82

CLUSTERING
In data mining, clustering is a method of partitioning data/
features into groups in such a way that each group contains
similar types of data. Statistical relationships and distance
measures are considered for partitioning data into different
clusters. Estimating the correct number of clusters,
however, may be a challenging task. To solve this issue, a
clustering approach based on the Ng-Jordan-Weiss (NJW)
algorithm is evaluated prior to estimating the number of
clusters, with the help of the visual assessment of cluster
tendency [128]. As a general rule for HSI classification
problems, if clustering is applied, the number of clusters
should be larger than the number of available classes in
the data set [43]. This derives from the presence of potentially
large numbers of objects in HSIs, especially at higher
spatial resolutions.
In recent years, several clustering-based BS approaches
have appeared [22], [75], [78], [118], [128], [130],
[133], [136], [178], [196], [128]. In [133] and [188], a
fuzzy clustering approach is used with particle swarm
optimization (PSO)-based optimization for optimal BS.
Here, k-means clustering [124], [185], [187], [198]-[201],
warped k-means [188], AP-based clustering [57], [103],
[125], [202], [203], orthogonal projection [204], sparsitybased
clustering [205], and divergence-based clustering
methods have been developed by constructing a hierarchical/graph
representation [100], [184] for BS. Several
distance measures associated with clustering have been
proposed in the literature, such as the dual cluster with
spectral and spatial angles [50], spatial cluster mean [43],
and instability index-based clustering [123], to mention
a few. Cosine dissimilarity-based local potential clustering
was proposed in [206], the ranking of which uses the
fast density-peak-based clustering (FDPC) method. The
latent low-rank representation model performs subspace
clustering for BS through random Hadamard projection,
offering inherent robustness against noise. Recently, the
Laplacian-regularized low-rank subspace clustering [92]
technique has proved its ability to preserve HSI global
structural information in selected bands. An SNN procedure
incorporates the weighted entropy-based k-nearestneighbor
search process to cluster the bands [207].
In clustering approaches, there exists a risk of creating
a " bad " cluster, which includes significantly noisy bands.
To tackle such a problem, a coarse-to-fine BS (CFBS) [79]
finds the set of bands by minimizing the error function
() (),
EZ eZiL=R
as defined in (11) and (12):
eZ min IZWI ZW
Wi
i () ()(),
=- -uu
T
ii ii
iEZIii i
i
st
=ar (),,gmin
, !!.. II IZand
Y
where Z represents the selected subset of bands, Ii
of HSI I, and Wi is the weight of Z .u
(11)
(12)
is a band
The CFBS approach iteratively groups bands with the help
of the linear reconstruction error and appends the most
significant band to update the optimal band set until the
desired number of bands is obtained. Because of the linear
reconstruction error objective, the CFBS technique is less
likely to select a noisy band, which can be an inherent advantage
of this approach.
Recently, a deep subspace clustering (DSC) technique
[108] was proposed,
incorporating spectral and spatial
information with the help of a convolutional autoencoder,
which it treats as a self-expressive layer. The encoder
and decoder functions are represented as
ID (, ),d
ni=EI e (, ) and
u = ni respectively. The DSC cost function L is represented
as
LUUCC C ,22 (13)
^h
ed
,,
ii am=- +- +
u
2 II
1
2
2
2
2
2
2
Selection
Strategy
Objective
Hybrid
Heuristic
Clustering
Correlation
NA
MI
Entropy
Ranking
Distance
NA
Selected
Optimal
Bands
FIGURE 8. Ranking and clustering with a selection strategy and an objective-driven heuristic strategy. NA: not attended.
82
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE SEPTEMBER 2021
IEEE Geoscience and Remote Sensing Magazine - September 2021

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