IEEE Geoscience and Remote Sensing Magazine - December 2021 - 53

convolutional autoencoder network to learn more informatic
features for clustering [158].
Random initialization is also often utilized for separated
network-based clustering models. For instance, in
[159], a CNN-based joint unsupervised learning (JSL) algorithm
was proposed. It starts with a random initialization
and formulates a recurrent framework to jointly update the
representations and clusters during the training process,
with clustering as the forward pass and representation as
the backward pass. In addition, a deep SSC (DSSC) method
was developed, which combines a DNN with SSC [160].
It randomly initializes the network and iteratively refines
the sparse coding and the clustering results in the forward
propagation stage, with the parameters of the DNN updated
in the backward propagation stage. Furthermore, a
DNN-based SC (SpectralNet) method was proposed [161].
It randomly initializes the parameters of the network and
considers three terms in the unsupervised training process:
1) affinity learning based on a Siamese network, 2)
embedding learning under an orthogonality constraint to
map the data into eigenspace, and 3) the clustering assignment.
As a result, it significantly outperforms traditional
SC methods.
GENERATIVE NETWORK-BASED CLUSTERING
Differing from autoencoder- and separated network-based
deep clustering methods, generative network-based clustering
approaches simultaneously perform clustering and
uncover the underlying structure of data to generate new
samples. These methods generally aim at learning the real
structure of data as accurately as possible to create highquality
samples. Therefore, they can more effectively guarantee
the discriminability of the extracted features. The
most representative generative deep clustering methods
can be the generative adversarial network (GAN)-based
approaches. These methods commonly include two parts,
i.e., the generator and the discriminator, and improve the
quality of the extracted features through the antagonism
between the generator and the discriminator. A typical
example is the categorical GAN (CatGAN) [162]. It plays
a minimum-maximum adversarial game to learn a discriminative
classifier in an unsupervised way, by trading
off mutual information between the observations and the
predicted class distribution. Its discriminator and generator
are defined as in (22):
LpyDh
E 6
D
max || ,Yi
zhh
GG
+ G
D
z
6
6
E
Yi
Lpnmi || ,,
G=-GG+^^ ^hh h66 6@@@ (22b)
G
py GD
yD
G
|, ,
Ez
py GD
z
where G $^h denotes the empirical entropy, y is the predicted
label of a given example ,Yi
and z is a generated noise
vector from a prior distribution P ,z^h with D and G representing
the discriminator and the generator, respectively.
Through adversarial learning, the CatGAN effectively
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
@ 66
@@
^
=-^
^^
py Dh@@
(22a)
enhances the discriminability and robustness of the classifier
and yields a high clustering accuracy.
Based on the CatGAN, in [163], an information-maximizing
GAN (InfoGAN) was proposed. It enhances the
clustering performance by exploiting the mutual information
among the fixed small subset of latent variables and
the observations. Furthermore, a deep adversarial GMM
autoencoder clustering (DAGMC) algorithm was developed
[164]. It uses an adversarial autoencoder network to learn
the reduced representations and employs a tunable GMM
for clustering. It simultaneously considers the autoencoder,
the GMM, and the adversarial losses in its objectives, which
are optimized by the stochastic gradient descend algorithm.
Moreover, a deep adversarial subspace clustering (DASC)
method was put forward [165]. It is also based on an adversarial
autoencoder network with a generator for subspace
estimation and the clustering assignment and a discriminator
for clustering performance evaluation. Then, it progressively
learns more informatic representations, with the selfrepresentation
and subspace clustering tasks supervised by
adversarial learning.
In addition to GAN-based models, a set of variational
autoencoder (VAE)-based generative deep clustering methods
has been developed, integrating certain probability
models into a deep network to learn the distribution of data
for sample generation. For example, in [166], a variational
deep embedding (VaDE) algorithm was proposed. It integrates
GMM into the VAE network for sample generation
and optimizes the clustering problem by maximizing the
evidence lower bound via the stochastic gradient variational
Bayes estimator. In addition, a VAE with Gaussian mixture
(VAE-GM) method was put forward [167]. It generates samples
from a prior distribution, i.e., Gaussian mixture, and
introduces the minimum information constraint to relieve
the over-regularization of VAE. As a result, it yields a high
clustering accuracy.
Overall, deep learning-based clustering methods can
bring about a higher clustering accuracy due to their powerful
feature learning and nonlinearity-fitting capabilities.
Accordingly, they have become a research hot spot in the
clustering field. However, most deep clustering methods are
concentrated in the computer vision field, with rare trails in
the hyperspectral remote sensing arena. Hence, more deep
learning-based hyperspectral clustering methods should
be developed to promote the development of this field. In
addition, most of the relevant works focus on improving
the clustering performance but ignoring the theoretical exploration
behind the performance, which leads to the poor
interpretability of these methods and limits their popularization
and application to a certain degree.
HYBRID MECHANISM-BASED CLUSTERING MODELS
Hybrid mechanism-based methods deal with the clustering
task by combining two or more models, as presented in
Figure 10. Considering that a single clustering model generally
has certain shortcomings, such techniques integrate
53
IEEE Geoscience and Remote Sensing Magazine - December 2021

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - December 2021
