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改进的水下声目标深度聚类模型
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Neural Process Lett
https://doi.org/10.1007/s11063-017-9755-7
An Improved Deep Clustering Model for Underwater
Acoustical Targets
Qiang Wang
1
· Lu Wang
1
· Xiangyang Zeng
1
·
Lifan Zhao
2
© Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract Hand-craft features and clustering algorithms constitute the main parts of the unsu-
pervised clustering system. Performance of the clustering deteriorates when the assumed
probabilistic distribution of the data differs from the true one. This paper introduces a novel
method that combines systematically the deep Boltzmann machine (DBM) with the Dirichlet
process based Gaussian mixture model (DP-GMM) to bypass the problem of distribution mis-
match. DBM is firstly used to extract the deep complex data features. By tactfully designing
the distributions of different layers in DBM to make them compatible to that of the DP-GMM,
we build a distribution consistent clustering system. The system is then jointly optimized by
Markov chain Monte Carlo method with succinct updating formulations. The experimental
results on two real databases of underwater acoustical target show the effectiveness and the
robustness of the proposed clustering method.
Keywords Data clustering · Deep Boltzmann machine · Dirichlet process · Gaussian
mixture model · Passive sonar target
B
Xiangyang Zeng
Qiang Wang
Lu Wang
Lifan Zhao
1
The School of Marine Science and Technology, Northwestern Polytechnical University,
Xi’an 710072, Shaanxi, China
2
The School of Electrical and Electronic Engineering, Nanyang Technological University,
Singapore 639798, Singapore
123
Q. Wang et al.
1 Introduction
Feature extraction and classification of underwater acoustical signal have attracted much
attention. Though the technology is considerably developed, automatic clustering system
has quite a big performance gap compared with human beings. The main difference comes
through the learning ways. Machine always works in a supervised way [6,7,12] while human
beings are always trained in an unsupervised way. Researchers [8,14] also show that the
powerful unsupervised pre-training can improve the performance of classification system.
Since the label information is generally unknown without human intervention in current
marine monitoring and the underwater acoustical signal recording system, it is of a great
demand for developing a powerful unsupervised clustering method with automatic feature
extraction.
Traditional unsupervised methods, such as k-means [5], Gaussian mixture model
(GMM) [3], etc., have several limitations in real applications. Firstly, those clustering meth-
ods are always trained with hand-craft features, such as, MFCC, which is a widely used
feature in the acoustic signal classification. However, those subjective hand-craft features
can be detrimental [20] when some discriminative information is wiped out by the improper
feature extraction procedures. Secondly, the number of classes needs to be predetermined in
many traditional clustering algorithms, which is generally impractical. Thirdly, the assumed
distribution in the clustering method may not well match to that of the extracted hand-craft
features. For instance, GMM and k-means assume that the samples of each class follow a
Gaussian distribution or standard Gaussian distribution [4]. However, the true distribution of
the hand-craft features may be quite complex and can not simply be expressed by Gaussian,
thus leading to a deteriorated clustering performance. Distribution mismatch can hardly be
avoided when the hand-craft features are considered in real applications.
Recently deep neural networks (DNN) provide alternative ways to reveal inherent struc-
ture of complex data and to extract discriminative features that outperform traditional
hand-craft ones. Such features extracted by DNN have become prevalent in clustering
and classification in many fields. There are several variants of DNN, such as (sparse)
autoencoders [10,11,21,23,24,26], convolutional neural network [13,25,27,28], deep belief
network [19], and so on. Among which, deep Boltzmann machine (DBM) has several
important characteristics: (1) DBM is a deep generative model which has a probabilistic
interpretation of data generation and can be trained in an entirely unsupervised manner. (2)
DBM reveals the inherent structure of the complex data and yields discriminative features
automatically. As demonstrated in recent studies, features extracted by DNN are more power-
ful than many hand-craft features. This fact will be also testified in our real data experiments
later in Sect. 3. (3) Most importantly, since DBM is probabilistic-based and can be applied to
generate output features with designated distribution, it can be systematically and coherently
combined with the Dirichlet process based Gaussian mixture model (DP-GMM) [15,17]
clustering method, where the distributions of the learned feature of DBM can match well
with that of DP-GMM to achieve an overall optimization of the clustering model.
In contrast to the traditional clustering system where feature extraction and clustering are
processed separately, we construct a fully automatic clustering system by coherently com-
bining the feature extraction with following clustering and develop an overall optimization
algorithm to achieve better clustering performance. In the proposed clustering system, two
subsystems, i.e., DBM and DP-GMM are well matched in the perspective of feature distribu-
tion and jointly optimized by Markov chain Monte Carlo (MCMC) based on the pre-designed
probabilistic model. In particular, the distributions of nodes on each layer of DBM are elabo-
123
An Improved Deep Clustering Model for Underwater…
Table 1 Symbols and notations
Symbol or notation Explanation
h
k
l
kth node of DBM in the lth layer. Element of vector h
l
W
(ij)
l
Weight between the ith node in the lth layer and jth node in the
(l + 1)th layer. Element of matrix W
l
μ
k
,
k
Parameters (mean vector and covariance matrix) of kth Gaussian
component
X Sample set with x
n
as the nth sample and X
k
as the kth cluster
DIR(π|α) Dirichlet distribution of variable π with parameter α
Mult(z|π) Multinomial distribution of variable z with parameter π
rately designed to match that of the DP-GMM method and the label assignment information
provided by the DP-GMM can be further feedback to train a better DBM. The promotive
interactions between the two aspects will be beneficial to learn better features and finally
obtain improved clustering performance. The contributions of this paper are mainly included
but not limited to:
– After pre-training of the subsystems, a joint optimization procedure to tune each subsys-
tem is developed by the Markov chain Monte Carlo (MCMC) method to achieve a global
optimization of the overall system. In the system, the distributions of nodes on each layer
of DBM are tactfully designed to achieve a simple but efficient sampling process.
– The subsystem DBM is designed to yield a Gaussian mixture distribution of output
layer to make sure that it well matched with the subsystem DP-GMM. It is worthy to
emphasized that the distribution mismatch is detrimental which will be demonstrated by
the real data experiments in the latter part of the letter.
Throughout this letter, bold symbols are used for vectors and matrices, while the corre-
sponding italics ones are their elements. |·| denotes the absolute operator.
S (x) represents
the sigmoid function 1/(e
−x
+ 1) for binary random variable x and N denotes the Gaus-
sian distribution. I is the identity matrix with a required dimension.
F is the fast Fourier
transformation (FFT). Other important notations are listed in Table 1.
The rest of this letter is structured as follows. The details of clustering system and learning
procedures are given in Sect. 2. In Sect. 3, real data experiments are conducted on two
underwater acoustical databases. Section 4 concludes the letter.
2 Deep Clustering Model
The proposed clustering system mainly composes of two parts: a L layers deep Boltzmann
machine and DP-GMM cluster, where the nodes on the output layer of DBM serve as the
inputs of the DP-GMM. The construction of our deep clustering system is illustrated in Fig. 1,
where two subsystems are collaboratively functioned as a whole by a joint optimization
procedure.
The inputs of the clustering system are the normalized spectra of the acoustical signals(see
Sect. 3.1). Obviously, Subsystems DBM and DP-GMM can be simply concatenated in a
cascading way. Firstly, DBM automatically learns the deep structure of the data from its
input according to the predefined probabilistic model and extracts the high-level feature with
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