IEEE Geoscience and Remote Sensing Magazine - December 2021 - 52
where f $^h and g $^h denote the nonlinear mapping function
of the encoder and the decoder, respectively;
, $^h
stands for the reconstruction loss function, defined as
,,
, =-^h
YX YXii ii 2
2
with Xi
being the reconstructed sample;
I represents the centroid matrix, with its ith column
referring to the ith cluster centroid; and si
means the assignment
vector with only one nonzero element. The first term
is the network loss, and the second term is the clustering
assignment loss, with c being a tradeoff parameter. Then,
the DCN solves this problem with an alternating stochastic
algorithm. Through learning more discriminative features
via a deep autoencoder network, the DCN outperforms traditional
clustering methods.
A set of deep clustering models has been developed
based on an autoencoder approach. In [148], a deep multimanifold
clustering (DMC) method was proposed. It integrates
a locality-preserving constraint into the deep autoencoder
network to learn the latent embedded manifolds
and more informatic features, using both the reconstruction
loss and the local preserving loss. Then, the proximity
of the representations to the centroids is employed as the
penalty to enhance the representations' clustering friendliness.
Furthermore, a dual autoencoder-based deep SC
(DAE-DSC) method was proposed that jointly optimizes
the deep autoencoder and the deep SC networks [149]. It
employs a dual autoencoder network to learn more robust
reduced representations and uses mutual information
to more effectively reserve discriminative information.
Moreover, a general deep clustering model was developed
by integrating the traditional clustering models, e.g., the
k-means and the GMM, into the deep networks [150]. It
yields a much higher accuracy than tradition methods.
The autoencoder was successfully introduced to subspace
clustering and delivered competitive performance by employing
deep networks to more effectively deal with feature
extraction and data nonlinearity simulation tasks. For example,
in [151], a deep subspace clustering algorithm based on
an autoencoder network (DSCNet) was proposed. It inserts
a self-expressive layer between the encoder and the decoder
to learn the pairwise adjacency between data points via back
propagation, and it integrates the reconstruction loss and the
self-representation loss to learn more discriminative representations.
In addition, a structured autoencoder-based subspace
clustering (StructAE) method was developed, which
constructs a structured autoencoder network to more effectively
preserve the local and global structure information of
data [152].
Furthermore, a self-supervised convolutional subspace
clustering network (S2ConvSCN) was put forward [153].
It employs a convolutional autoencoder network to fully
explore the spatial information of an image, and it adds a
self-expression module and an SC module into the network
to generate a trainable end-to-end model. Then, it jointly
optimizes the feature extraction and subspace clustering in
a self-supervised way. Moreover, the LRDSC algorithm introduced
previously obtains a higher clustering accuracy for
52
SEPARATED NETWORK-BASED CLUSTERING
Separated network-based clustering methods generally optimize
a deep network only by the clustering loss, with the
network and the clustering model separated. Although the
basic network can be very deep, these methods may fail to
learn informatic features for clustering, due to the absence
of a network constraint, such as the reconstruction loss.
Therefore, the initialization of the network seems crucial
for these methods. Generally, the network is pretrained or
randomly initialized. A typical example is clustering based
on CNN (CCNN) [155]. It deals with the feature extraction
and clustering tasks within the CNN framework in an iterative
way. First, it employs a CNN pretrained on ImageNet
to extract features for initial clustering, with c randomly selected
centroids and the minibatch k-means utilized. Then,
it exploits the difference between the label predicted by the
CNN and the minibatch k-means to fine-tune the network,
based on the stochastic gradient descent algorithm, and simultaneously
updates the cluster centroids, as in (21). The
CCNN employs feature drift compensation to relieve mismatching
to further improve the clustering accuracy:
c
2 yt ,
1
jj
j
j =1
nnjcc=^^^
j
1
khhh
k-1
+
j
h
^ h
k
new
,
where SSE denotes the sum of the squared error; yj
n^h
k
j
new
^h
(21b)
and tj
stand for the label predicted by the CNN and the minibatch
k-means, respectively;
kth iteration; h k
represents the jth centroid in the
indicates the extracted features from a
minibatch assigned to ;jn and jc is the learning rate of the
jth centroid, which is defined as the reciprocal of the number
of samples in the jth cluster.
Unsupervised pretraining is widely utilized for separated
network-based clustering methods. In [156], a deep
brief network (DBN) nonparametric clustering (DBNC) algorithm
was proposed that relies on an unsupervised pretrained
DBN. It learns the reduced representations of data
through the pretrained DBN and employs nonparametric
clustering with the maximum margin to perform clustering,
with the parameters of the top layer of the DBN finetuned
subsequently. In addition, a deep embedded clustering
(DEC) method was developed [157]. It first pretrains a
stacked autoencoder network, based on the reconstruction
loss in an unsupervised way, and drops the decoder part.
Then, it fine-tunes the network with the clustering loss and
refines the clustering result based on the Kullback-Leibler
divergence between the soft assignment and the auxiliary
distribution in an iterative way. Based on the DEC model,
an improved version was put forward, by employing a
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2021
SSE= /^h2
-
(21a)
HSIs by introducing a convolutional autoencoder to subspace
clustering [137]. In addition, in [154], a deep subspace
clustering band selection model was developed for HSIs,
combining a convolutional autoencoder network with the
SSC model and producing a good band selection effect.
IEEE Geoscience and Remote Sensing Magazine - December 2021
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