IEEE Geoscience and Remote Sensing Magazine - December 2021 - 51

where K $^h denotes the kernelized data matrix, with the
Gaussian radial basis function commonly utilized.
A typical kernel subspace clustering method is the kernel
SSC algorithm with a spatial maximum pooling operation
(KSSC-SMP) [142]. The KSSC-SMP extends SSC to nonlinear
manifolds to construct the KSSC model to relieve the
nonlinearly separable problem of HSIs to some degree. Then,
it incorporates spatial neighborhood information through
spatial maximum pooling to generate more discriminative
features. Consequently, the KSSC-SMP may outperform linear
SSC methods. In addition, in [143], a kernel sparse and
LRSC (KSLRSC) algorithm was proposed. It utilizes sparse
and low-rank constraints to simultaneously explore the local
and global structure information of HSIs. Accordingly, the
underlying adjacency among pixels can be more accurately
learned. Then, the KSLRSC method is extended to semisupervised
classification for HSIs. Furthermore, by adding a
TV denoising constraint into the KSSC model to enhance
the similarity among pixels from the same subspace, a KSSC
with TV denoising (KSSC-TVD) algorithm was put forward
for HSIs [144]. In addition, the k-SSMLC method is also a
typical kernel subspace clustering model [140], which extends
the linear multiview subspace clustering model to a
kernel version to further improve the clustering accuracy.
In general, because of accurate modeling and powerful information
extraction capability, subspace clustering methods
have shown great potential for HSI clustering and achieved
very competitive performance. In recent years, subspace clustering
has gained progressively more attention. However,
such methods are generally accompanied by a large computational
complexity and massive time and memory consumption,
which limits their applications to some degree.
DEEP LEARNING-BASED CLUSTERING METHODS
Deep learning-based clustering methods have been recently
developed and are one of the most advanced clustering techniques
[145]. These approaches rely on deep NNs (DNNs),
such as fully connected networks (FCNs) and convolutional
NNs (CNNs), to learn more discriminative features for clustering
and to more accurately simulate the nonlinearity of
data, as shown in Figure 9. Such methods generally deploy
two components, i.e., the network and the clustering model.
Since there are no available labeled samples, these models
are generally optimized in an unsupervised way. According
to the basic architecture, deep learning-based clustering
methods can be further divided into three main categories:
1) autoencoder-based clustering, 2) separated network-based
clustering, and 3) generative network-based clustering [146].
AUTOENCODER-BASED CLUSTERING
Autoencoder-based clustering methods are the earliest and
most representative deep clustering approaches. An autoencoder
is an unsupervised NN with the advantages of
simplicity and effectiveness. It generally consists of an encoder
for data representation and a decoder for data reconstruction,
and it self-trains by minimizing the reconstruction
error. A typical example is the deep clustering network
IEEE Geoscience and Remote Sensing Magazine - December 2021

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