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Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

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Front. Comput. Sci.    2023, Vol. 17 Issue (3) : 173322    https://doi.org/10.1007/s11704-022-1376-2
RESEARCH ARTICLE
Heterogeneous clustering via adversarial deep Bayesian generative model
Xulun YE(), Jieyu ZHAO
Institute of Computer Science and Technology, Ningbo University, Ningbo 315211, China
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Abstract

This paper aims to study the deep clustering problem with heterogeneous features and unknown cluster number. To address this issue, a novel deep Bayesian clustering framework is proposed. In particular, a heterogeneous feature metric is first constructed to measure the similarity between different types of features. Then, a feature metric-restricted hierarchical sample generation process is established, in which sample with heterogeneous features is clustered by generating it from a similarity constraint hidden space. When estimating the model parameters and posterior probability, the corresponding variational inference algorithm is derived and implemented. To verify our model capability, we demonstrate our model on the synthetic dataset and show the superiority of the proposed method on some real datasets. Our source code is released on the website: Github.com/yexlwh/Heterogeneousclustering.
Keywords dirichlet process      heterogeneous clustering      generative adversarial network      laplacian approximation      variational inference     
Corresponding Author(s): Xulun YE   
Just Accepted Date: 27 April 2022   Issue Date: 07 November 2022
 Cite this article:   
Xulun YE,Jieyu ZHAO. Heterogeneous clustering via adversarial deep Bayesian generative model[J]. Front. Comput. Sci., 2023, 17(3): 173322.
 URL:  
https://academic.hep.com.cn/fcs/EN/10.1007/s11704-022-1376-2
https://academic.hep.com.cn/fcs/EN/Y2023/V17/I3/173322
Notations Descriptions
K^ Ground truth of the cluster number
Xs Samples in the s space
Xt Samples in the t space
X Samples which ignores the feature space
δis(),δit() Permutation function defined at xis and xit
Tst Metric measures feature space s and t
Tss,Ttt Metric of feature space s (t) and s (t)
T Heterogeneous metric
L Graph Laplacian of T
Seq() Structure order sequence
c0,u0,v0,B0 Hyper parameter for G0
Ω Hidden variables for the BHAC
α Hyper parameter for DP
Ψ() Digamma function
DP() Dirichlet process (DP)
GN() GAN generative network
DN() GAN discriminative network
K Maximum cluster number
zn Cluster indicator
γk,τk,?n Variational parameters
w~n Laplacian approximation parameters
Tab.1  The main notations and descriptions
Fig.1  Illustration of data structure with different features. The 1st row is the original images. The 2nd row shows the images with different light conditions. The 3rd row demonstrates the images with sift feature. Right figure illustrates the feature distribution in the 3D space. From the figure, we know that data with different feature share the same data structure
  
Fig.2  Overview of the optimization process of the proposed deep Bayesian generative network
  
Fig.3  Illustration of BHAC clustering result on the synthetic dataset. (a) and (b) demonstrate the original dataset without class labels; (c) and (d) are the BHAC results
Data COIL20 COIL100 BALLET USPS MNIST
Feature Original image+noise rotated image
D 100 100 130 70 30
K 70 130 60 60 50
Feature Original image+SIFT
D 90 90 60 90 40
K 70 130 110 70 40
Tab.2  Parameters used in the five real datasets
Method COIL20 COIL100 BALLET USPS MNIST COIL20 COIL100 BALLET USPS MNIST
Feature Original image+noise rotated Image Original image+SIFT+TNT
BHAC 0.51 0.54 0.45 0.49 0.47 0.61 0.55 0.23 0.41 0.41
DP-space 0.07 0.02 0.07 0.02 0.01 0.02 0.02 0.01 0.05 0.02
SCAMS 0.26 0.24 0.15 0.07 0.24 0.08 0.03 0.04 0.05 0.11
AutoSC-N 0.22 0.18 0.17 0.18 0.21 0.01 0.12 0.13 0.09 0.13
CFSFDP 0.17 0.21 0.29 0.21 0.34 0.36 0.17 0.19 0.21 0.21
DPM 0.05 0.12 0.03 0.03 0.26 0.06 0.04 0.03 0.07 0.11
GFMM 0.01 0.06 0.04 0.08 0.04 0.04 0.02 0.02 0.06 0.03
BLRASC 0.41 0.03 0.11 0.30 0.37 0.29 0.22 0.27 0.24 0.03
ACIDS 0.32 0.39 0.26 0.32 0.42 0.33 0.13 0.39 0.10 0.17
ClusterGAN 0.27 0.17 0.04 0.23 0.47 0.11 0.13 0.01 0.14 0.04
Spectral-Net 0.29 0.32 0.35 0.28 0.39 0.34 0.17 0.36 0.22 0.21
Feature Original image+noise rotated image+DAMA Original image+SIFT+CDLS
DP-space 0.04 0.12 0.02 0.07 0.03 0.06 0.01 0.02 0.02 0.04
SCAMS 0.26 0.25 0.14 0.21 0.27 0.11 0.02 0.02 0.01 0.02
AutoSC-N 0.31 0.37 0.11 0.23 0.31 0.31 0.07 0.06 0.14 0.12
CFSFDP 0.21 0.24 0.17 0.31 0.37 0.39 0.12 0.27 0.21 0.17
DPM 0.17 0.09 0.04 0.06 0.31 0.31 0.02 0.03 0.05 0.13
GFMM 0.12 0.16 0.02 0.06 0.02 0.03 0.01 0.01 0.01 0.04
BLRASC 0.39 0.42 0.27 0.34 0.44 0.37 0.21 0.11 0.17 0.12
ACIDS 0.41 0.44 0.27 0.27 0.51 0.42 0.11 0.36 0.13 0.14
ClusterGAN 0.36 0.32 0.05 0.38 0.58 0.07 0.04 0.07 0.08 0.02
Spectral-Net 0.31 0.40 0.22 0.35 0.54 0.34 0.09 0.29 0.12 0.17
Ground truth 20.0 100.0 44.0 10.0 10.0 20.0 100.0 44.0 10.0 10.0
Estimated number 31.2 127.6 60.4 20.2 21.2 25.1 125.2 7.1 30.1 17.1
Tab.3  Clustering accuracy (NMI) and the estimated cluster number on the real world datasets
Fig.4  Illustration of generated images with the COIL20 and BALLET dataset. (a) and (d) demonstrate the samples from original data. (b) and (e) show the samples with the noise and rotation. (c) and (f) are the images generated from our model
Data COIL20 COIL100 BALLET USPS MNIST COIL20 COIL100 BALLET USPS MNIST
Feature Original image+noise rotated image Original image+SIFT
Time 4813.5 22620.6 78160.3 67296.3 222426.7 3210.2 13108.1 34047.5 35915.9 110821.2
Tab.4  Running time on the five real datasets (seconds)
Fig.5  Illustration of the clustering result of the BHAC parameter effect on the COIL20, COIL100 and BALLET dataset. The 1st two figures (a) and (b) show the clustering accuracy (NMI), while the last two figures (c) and (d) demonstrates the estimated cluster number
Method COIL20 COIL100 BALLET
Same parameters 1.51 2.12 0.69
Hyper parameter α 1.67 2.02 0.68
Different stretagy 6.55 15.62 3.67
K 7.20 38.33 0.84
D 6.31 41.32 0.54
Tab.5  Variance of the estimated cluster number
  
  
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