ZHU Hongyan and ZHAI Qiaozhu, “A Global Optimal Gaussian Mixture Reduction Approach Based on Integer Linear Programming,” Chinese Journal of Electronics, vol. 22, no. 4, pp. 763-768, 2013,
Citation: ZHU Hongyan and ZHAI Qiaozhu, “A Global Optimal Gaussian Mixture Reduction Approach Based on Integer Linear Programming,” Chinese Journal of Electronics, vol. 22, no. 4, pp. 763-768, 2013,

A Global Optimal Gaussian Mixture Reduction Approach Based on Integer Linear Programming

Funds:  This work is supported by the National Natural Science Foundation of China (No.61203220, No.61174146), the Program for New Century Talents of Education Ministry (No.NCET-08-0432), and the Foundation for Authors of National Outstanding Doctoral Dissertation (No.201047).
More Information
  • Corresponding author: ZHU Hongyan, ZHAI Qiaozhu
  • Received Date: 2012-09-01
  • Rev Recd Date: 2013-01-01
  • Publish Date: 2013-09-25
  • In many applications, the Gaussian mixture serves as an important probabilistic representation of the system state. A global optimal Gaussian mixture reduction (GMR) approach based on Integer linear programming (ILP) is developed in this paper. Firstly, a Gaussian base set is constructed with partial merging of components of the original mixture. Secondly, by introducing auxiliary variables reasonably, the original problem of selecting the best candidates from the given Gaussian base set is formulated as an ILP problem. Finally, a global optimal solution to GMR is obtained by solving the ILP problem. The global optimum property enables it as a basis for performance comparison with different GMR algorithms.
  • loading
  • J.M.C. Clark, P.A. Kountouriotis and R.B. Vinter, “A Gaussianm ixture filter for range-only tracking”, IEEE Transactions onA utomatic Control, Vol.56, No.3, pp.602-613, 2011.
    I.Y. Ozbek, M. Hasegawa-Johnson and M. Demirekler, “Estimation of articulatory trajectories based on Gaussian mixturem odel (GMM) with audio-visual information fusion andd ynamic Kalman smoothing”, IEEE Transactions on Audio,S peech, and Language Processing, Vol.19, No.5, pp.1180-1195,2 011.
    D. Hosseinzadeh and S. Krishnan, “Gaussian mixture modeling of keystroke patterns for biometric applications”, IEEE Transactionso n Systems, Man, and Cybernetics, Part C: Applications and Reviews, Vol.38, No.6, pp.816-826, 2008.
    H. Greenspan, J. Goldberger and A. Mayer, “Probabilistics pace-time video modeling via piecewise GMM”, IEEE Transactionso n Pattern Analysis and Machine Intelligence, Vol.26,N o.3, pp.384-396, 2004.
    A. Nikseresht and M. Gelgon, “Gossip-based computation of aG aussian mixture model for distributed multimedia indexing”,I EEE Trans on Multimedia, Vol.10, No.3, pp.85-392, 2008.
    B. Li, W.J. Liu and L.H. Dou, “Unsupervised learning of Gaussianm ixture model with application to image segmentation”, Chinese Journal of Electronics, Vol.19, No.3, pp.451-456, 2010.
    D.J. Salmond, “Mixture reduction algorithms for target trackingi n clutter”, Proceedings of SPIE: Signal and Data Processing of Small Targets Conference, Vol.1305, pp.434-445, 1990.
    D.J. Salmond, “Mixture reduction algorithms for point and extendedo bject tracking in clutter”, IEEE Trans on AES, Vol.45,N o.2, pp.667-686, 2009.
    D.W. Scott and W.F. Szewczyk, “From kernels to mixtures”,T echnometrics (Special Tukey Memorial Issue), Vol.43, No.3,p p.323-335, 2001.
    J.E. Harmse, “Reduction of Gaussian mixture models by maximums imilarity”, Journal of Nonparametric Statistics, Vol.22,N o.6, pp.703-709, 2010.
    J.L. Williams and P.S. Maybeck, “Cost-function based hypothesisc ontrol techniques for multiple hypothesis tracking”, Mathematical and Computer Modelling, Vol.43, No.9, pp.976-989,2 006.
    J.L. Williams, “Gaussian mixture reduction for trackingm ultiple maneuvering targets in clutter”, http://www.dtic.mil/srch/doc?collection=t3&id=ADA415317,2003-03-01.
    D.J. Petrucci, “Gaussian mixture reduction for Bayesian targett racking in clutter”, http://www.dtic.mil/srch/doc?collection=t3&id=ADA443588, 2005-12-01.
    A.R. Runnalls, “Kullback-Leibler approach to Gaussian mixturer eduction”, IEEE Trans on AES, Vol.43, No.3, pp.989-999,2 007.
    D. Schieferdecker and M.F. Huber, “Gaussian mixture reductionv ia clustering”, Proceedings of the 11th International Conferenceo n information Fusion, Seattle, WA, pp.1536-1543, 2009.
    H. Chen, K.C. Chang, and C. Smith, “Constraint optimizedw eight adaptation or Gaussian mixture reduction”, Proceedings of SPIE: Signal Processing, Sensor Fusion, and Target RecognitionX IX, Vol.7697, Orlando, FL, pp.76 970N176 970N10, 2010.
    M.F. Huber and U.D. Hanebeck, “Progressive Gaussian mixturer eduction”, Proceedings of 10th International Conferenceo n information Fusion, Cologne, Germany, pp.1-8, 2008.
    D.F. Crouse, P. Willett, K. Pattipati and L. Svensson, “A Look at Gaussian mixture reduction algorithms”, Proceedings of 14th International Conference on Information Fusion, Chicago,U SA, pp.570-577, 2011.
    P. Bruneau, M. Gelgo and F. Picarougne, “Parsimonious reduction of Gaussian mixture models with a variational-Bayes approach”, Pattern Recognition, Vol.43, No.3, pp.850-858, 2010.
    C. Bishop, Pattern Recognition and Machine Learning, Cambridge,U .K, Springer, 2006.
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (399) PDF downloads(1325) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint