Bounded generalized Gaussian mixture model

Abstract The generalized Gaussian mixture model (GGMM) provides a flexible and suitable tool for many computer vision and pattern recognition problems. However, generalized Gaussian distribution is unbounded. In many applications, the observed data are digitalized and have bounded support. A new bounded generalized Gaussian mixture model (BGGMM), which includes the Gaussian mixture model (GMM), Laplace mixture model (LMM), and GGMM as special cases, is presented in this paper. We propose an extension of the generalized Gaussian distribution in this paper. This new distribution has a flexibility to fit different shapes of observed data such as non-Gaussian and bounded support data. In order to estimate the model parameters, we propose an alternate approach to minimize the higher bound on the data negative log-likelihood function. We quantify the performance of the BGGMM with simulations and real data.

[1]  Lorenzo Bruzzone,et al.  An unsupervised approach based on the generalized Gaussian model to automatic change detection in multitemporal SAR images , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[2]  Aly A. Farag,et al.  Precise segmentation of multimodal images , 2006, IEEE Transactions on Image Processing.

[3]  Martin Vetterli,et al.  Adaptive wavelet thresholding for image denoising and compression , 2000, IEEE Trans. Image Process..

[4]  Miin-Shen Yang,et al.  A robust EM clustering algorithm for Gaussian mixture models , 2012, Pattern Recognit..

[5]  Guoqing Liu,et al.  Probabilistic classifiers with a generalized Gaussian scale mixture prior , 2013, Pattern Recognit..

[6]  Jonas Samuelsson,et al.  Bounded support Gaussian mixture modeling of speech spectra , 2003, IEEE Trans. Speech Audio Process..

[7]  Zhen Yang,et al.  The infinite Student's t-factor mixture analyzer for robust clustering and classification , 2012, Pattern Recognit..

[8]  Anil K. Jain,et al.  Statistical Pattern Recognition: A Review , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[10]  Mohand Saïd Allili,et al.  Wavelet Modeling Using Finite Mixtures of Generalized Gaussian Distributions: Application to Texture Discrimination and Retrieval , 2012, IEEE Transactions on Image Processing.

[11]  Geoffrey J. McLachlan,et al.  Robust mixture modelling using the t distribution , 2000, Stat. Comput..

[12]  Chong-Sze Tong,et al.  Statistical Wavelet Subband Characterization Based on Generalized Gamma Density and Its Application in Texture Retrieval , 2010, IEEE Transactions on Image Processing.

[13]  Andrew R. Webb,et al.  Statistical Pattern Recognition , 1999 .

[14]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[15]  Q. M. Jonathan Wu,et al.  An Extension of the Standard Mixture Model for Image Segmentation , 2010, IEEE Transactions on Neural Networks.

[16]  W. Rudin.  Real and complex analysis , 1968 .

[17]  Jan Skoglund,et al.  Vector quantization based on Gaussian mixture models , 2000, IEEE Trans. Speech Audio Process..

[18]  Pierre Moulin,et al.  Analysis of Multiresolution Image Denoising Schemes Using Generalized Gaussian and Complexity Priors , 1999, IEEE Trans. Inf. Theory.

[19]  Minh N. Do,et al.  Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance , 2002, IEEE Trans. Image Process..

[20]  Ulrich Stadtmüller,et al.  Multivariate boundary kernels and a continuous least squares principle , 1999 .

[21]  Mohamed A. Deriche,et al.  A novel fingerprint image compression technique using wavelets packets and pyramid lattice vector quantization , 2002, IEEE Trans. Image Process..

[22]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[23]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .