skip to main content
research-article

Gaussian Mixture Model Clustering with Incomplete Data

Published: 31 March 2021 Publication History

Abstract

Gaussian mixture model (GMM) clustering has been extensively studied due to its effectiveness and efficiency. Though demonstrating promising performance in various applications, it cannot effectively address the absent features among data, which is not uncommon in practical applications. In this article, different from existing approaches that first impute the absence and then perform GMM clustering tasks on the imputed data, we propose to integrate the imputation and GMM clustering into a unified learning procedure. Specifically, the missing data is filled by the result of GMM clustering, and the imputed data is then taken for GMM clustering. These two steps alternatively negotiate with each other to achieve optimum. By this way, the imputed data can best serve for GMM clustering. A two-step alternative algorithm with proved convergence is carefully designed to solve the resultant optimization problem. Extensive experiments have been conducted on eight UCI benchmark datasets, and the results have validated the effectiveness of the proposed algorithm.

References

[1]
Elie Aljalbout, Vladimir Golkov, Yawar Siddiqui, and Daniel Cremers. 2018. Clustering with deep learning: Taxonomy and new methods. arXiv: Learning (2018).
[2]
Marco Aste, Massimo Boninsegna, Antonino Freno, and Edmondo Trentin. 2015. Techniques for dealing with incomplete data: A tutorial and survey. Pattern Analysis and Applications 18, 1 (2015), 1–29.
[3]
Steffen Bickel and Tobias Scheffer. 2004. Multi-view clustering. In Fourth IEEE International Conference on Data Mining (ICDM'04). 19–26.
[4]
Charles A. Bouman, Michael Shapiro, G. W. Cook, C. Brian Atkins, and Hui Cheng. 1997. Cluster: An Unsupervised Algorithm for Modeling Gaussian Mixtures. Technical Report.
[5]
Magalie Celton, Alain Malpertuy, Gaëlle Lelandais, and Alexandre G. De Brevern. 2010. Comparative analysis of missing value imputation methods to improve clustering and interpretation of microarray experiments. BMC Genomics 11, 1 (2010), 15.
[6]
Liang Du, Peng Zhou, Lei Shi, Hanmo Wang, Mingyu Fan, Wenjian Wang, and Yi-Dong Shen. 2015. Robust multiple kernel -means clustering using -norm. In International Joint Conference on Artificial Intelligence (IJCAI'15). 3476–3482.
[7]
Eduard Eiben, Robert Ganian, Iyad Kanj, Sebastian Ordyniak, and Stefan Szeider. 2019. On clustering incomplete data. arXiv preprint arXiv:1911.01465 (2019).
[8]
Payam Ezatpoor, Justin Zhan, Jimmy Ming-Tai Wu, and Carter Chiu. 2018. Finding top- dominance on incomplete big data using Mapreduce framework. IEEE Access 6 (2018), 7872–7887.
[9]
Pedro J. García-Laencina, José-Luis Sancho-Gómez, Aníbal R. Figueiras-Vidal, and Michel Verleysen. 2009. K nearest neighbours with mutual information for simultaneous classification and missing data imputation. Neurocomputing 72, 7–9 (2009), 1483–1493.
[10]
Zoubin Ghahramani and Michael I. Jordan. 1994. Supervised learning from incomplete data via an EM approach. In Advances in Neural Information Processing Systems. 120–127.
[11]
Iffat A. Gheyas and Leslie S. Smith. 2010. A neural network-based framework for the reconstruction of incomplete data sets. Neurocomputing 73, 16–18 (2010), 3039–3065.
[12]
Xifeng Guo, Long Gao, Xinwang Liu, and Jianping Yin. 2017. Improved deep embedded clustering with local structure preservation. In International Joint Conference on Artificial Intelligence (IJCAI'17). 1753–1759.
[13]
John A. Hartigan. 1975. Clustering Algorithms. John Wiley & Sons, Inc.
[14]
Shao-Yuan Li, Yuan Jiang, and Zhi-Hua Zhou. 2014. Partial multi-view clustering. In Association for the Advance of Artificial Intelligence (AAAI'14). 1968–1974.
[15]
Tianhao Li, Liyong Zhang, Wei Lu, Hui Hou, Xiaodong Liu, Witold Pedrycz, and Chongquan Zhong. 2017. Interval kernel fuzzy C-means clustering of incomplete data. Neurocomputing 237 (2017), 316–331.
[16]
Xinwang Liu, Yong Dou, Jianping Yin, Lei Wang, and En Zhu. 2016. Multiple kernel k-means clustering with matrix-induced regularization. In Association for the Advance of Artificial Intelligence (AAAI'16). 1888–1894.
[17]
Xinwang Liu, Wen Gao, Xinzhong Zhu, Miaomiao Li, Lei Wang, En Zhu, Tongliang Liu, Marius Kloft, Dinggang Shen, and Jianping Yin. 2020. Multiple kernel k-means with incomplete kernels. IEEE Transactions on Pattern Analysis and Machine Intelligence 42, 5 (2020), 1191–1204.
[18]
Xinwang Liu, Lei Wang, Xinzhong Zhu, Miaomiao Li, En Zhu, Tongliang Liu, Li Liu, Yong Dou, and Jianping Yin. 2020. Absent multiple kernel learning algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence 42, 6 (2020), 1303–1316.
[19]
Volodymyr Melnykov and Ranjan Maitra. 2010. Finite mixture models and model-based clustering. Statistics Surveys 4 (2010), 80–116.
[20]
Erxue Min, Xifeng Guo, Qiang Liu, Gen Zhang, Jianjing Cui, and Jun Long. 2018. A survey of clustering with deep learning: From the perspective of network architecture. IEEE Access 6 (2018), 39501–39514.
[21]
Chunfeng Song, Feng Liu, Yongzhen Huang, Liang Wang, and Tieniu Tan. 2013. Auto-encoder based data clustering. In Iberoamerican Congress on Pattern Recognition (CIARP'13). 117–124.
[22]
Anusua Trivedi, Piyush Rai, Hal Daumé III, and Scott L. DuVall. 2010. Multiview clustering with incomplete views. In NIPS Workshop, Vol. 224.
[23]
Siwei Wang, Miaomiao Li, Ning Hu, En Zhu, Jingtao Hu, Xinwang Liu, and Jianping Yin. 2019. K-means clustering with incomplete data. IEEE Access 7 (2019), 69162–69171.
[24]
Yang Wang, Xuemin Lin, Lin Wu, Wenjie Zhang, Qing Zhang, and Xiaodi Huang. 2015. Robust subspace clustering for multi-view data by exploiting correlation consensus. IEEE Transactions on Image Processing 24, 11 (2015), 3939–3949.
[25]
Y. Wang, L. Wu, X. Lin, and J. Gao. 2018. Multiview spectral clustering via structured low-rank matrix factorization. IEEE Transactions on Neural Networks and Learning Systems 29, 10 (2018), 4833–4843.
[26]
Lin Wu, Yang Wang, and Ling Shao. 2019. Cycle-consistent deep generative hashing for cross-modal retrieval. IEEE Transactions on Image Processing 28, 4 (2019), 1602–1612.
[27]
Cong-Hua Xie, Jin-Yi Chang, and Yong-Jun Liu. 2013. Estimating the number of components in Gaussian mixture models adaptively for medical image. Optik 124, 23 (2013), 6216–6221.
[28]
Junyuan Xie, Ross Girshick, and Ali Farhadi. 2016. Unsupervised deep embedding for clustering analysis. In International Conference on Machine Learning (ICML'16). 478–487.
[29]
Rui Xu and Donald Wunsch. 2005. Survey of clustering algorithms. IEEE Transactions on Neural Networks 16, 3 (2005), 645–678.
[30]
Shi Yu, Léon-Charles Tranchevent, Xinhai Liu, Wolfgang Glänzel, Johan A. K. Suykens, Bart De Moor, and Yves Moreau. 2012. Optimized data fusion for kernel k-means clustering. IEEE TPAMI 34, 5 (2012), 1031–1039.
[31]
En Zhu, Sihang Zhou, Yueqing Wang, Jianping Yin, Miaomiao Li, Xinwang Liu, and Yong Dou. 2017. Optimal neighborhood kernel clustering with multiple kernels. In Association for the Advance of Artificial Intelligence (AAAI'17). 2266–2272.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Multimedia Computing, Communications, and Applications
ACM Transactions on Multimedia Computing, Communications, and Applications  Volume 17, Issue 1s
January 2021
353 pages
ISSN:1551-6857
EISSN:1551-6865
DOI:10.1145/3453990
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 31 March 2021
Accepted: 01 June 2020
Revised: 01 May 2020
Received: 01 April 2020
Published in TOMM Volume 17, Issue 1s

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. GMM
  2. clustering
  3. EM
  4. incomplete data

Qualifiers

  • Research-article
  • Refereed

Funding Sources

  • National Natural Science Foundation of China

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)291
  • Downloads (Last 6 weeks)35
Reflects downloads up to 03 Mar 2025

Other Metrics

Citations

Cited By

View all

View Options

Login options

Full Access

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

HTML Format

View this article in HTML Format.

HTML Format

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media