IEEE Geoscience and Remote Sensing Magazine - December 2021 - 42

c
pp ,
j =1
^^ ^hh h
YY Pj|| ,~i ~j
i H = /
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ij
(6a)
(6b)
where H ii f i @ is the class parameter set and P j^h~ is
the prior probability of the jth class ~ Then, the independent
components and the mixing matrix of each class are estimated
based on the modified information maximum model, and
the membership probability of each pixel to belong to various
classes is computed. Based on the maximum membership
probability rule, the pixel partition result can be obtained
based on the ICA model. A weighted principle component
analysis ICA (WPCA-ICA) method was developed to extract
the independent features based on second- and higher-order
statistics, which performs better for HSIs [82].
Furthermore, in [83], a nonparametric stochastic expectation
maximum (NPSEM) algorithm was proposed, which
extends stochastic EM to a nonparametric representation
to further improve the model's practicability. The NPSEM
was then introduced to HSIs and performed well [36]. In
[84], a pairwise Markov field (PMF) model was constructed
to segment noisy and blurred astronomical HSIs. It integrates
the PMF model into the Bayesian framework to optimize
the probability model, and it segments HSIs based
on faint singles. In addition, to better learn the similarity
among hyperspectral pixels, a layered sparse adaptive
possibility c-means clustering (LSAPCM) approach was
developed [85]. It integrates the layered possibility into the
FCM framework to extend the architecture to a probability
optimization model, and it produces good clustering results.
In [86], a novel clustering model based on the latent Dirichlet
distribution (CLDD) was constructed by introducing the
topic model to simulate the structure of HSIs, with each topic
modeled by the LDD.
Moreover, considering that the mixed pixels of HSIs generally
degrade the GMM performance, a Bayesian clustering
method based on the spectral mixture model (SMM)
and the Markov random field (MRF) was put forward for
HSIs [87]. The Bayesian SMM-MRF utilizes the SMM to obtain
the end-member abundance for each mixed pixel, and
it assigns the mixed pixel according to the dominant endmember.
Subsequently, this method integrates the SMM
into the Bayesian framework to construct a conditional distribution
of the mixed pixels to search for the dominant
end-member, with the MRF utilized to optimize the label
prior. Last, by solving the maximum posterior probability
problem based on the EM rule, the pixel partition result
is obtained. By considering the mixed pixel problem and
comprehensively utilizing spectral-spatial
information,
the Bayesian SMM-MRF achieves good performance.
As a whole, probability-based clustering methods have
strict mathematical foundations and employ various probability
theories to optimize the clustering model. However, the
complex internal structure and large spectral variability of HSIs
make hyperspectral pixels not strictly obey specific probability
distributions, and thus they are inconsistent with the assumptions
of such methods. As a result, probability-based clustering
methods may fail to obtain good performance for HSIs.
BIONICS-BASED CLUSTERING METHODS
Bionics-based clustering methods employ certain biological
models, such as artificial neural networks (NNs), to
simulate the complex internal structure of HSIs and partition
pixels based on certain biological evolution algorithms,
as described in Figure 5. A typical example is the
self-organizing map (SOM) model, which is an unsupervised
learning method based on the Kohonen NN and
has been successfully applied to HSIs [42], [88]. The SOM
automatically learns the underlying similarity among the
input pixels and then puts similar pixels close together in
the network. The SOM generally consists of an input layer
and a competitive layer, with a learning stage and a clustering
stage. In the learning stage, the winning neurons are
selected based on Euclidean distance, and then the weights
of the winning neurons and the neighboring neurons are
0.04
0.02
20
10
(a)
0 0
(b)
10
(c)
FIGURE 4. The probability-based clustering mechanism. (a) The HSI. (b) The probability model construction and optimization. (c) The
clustering result.
42
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IEEE Geoscience and Remote Sensing Magazine - December 2021

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