Bayesian estimation of generalized Gamma mixture model based on variational EM algorithm
•We propose a VEM algorithm for the inference of the generalized Gamma mixture model (GMM) with all the closed-form update equations.•The help function is used to approximate the lower bound of the variational objective function in GMM.•With the proposed VEM algorithm, the effective number of compon...
Saved in:
| Published in: | Pattern recognition Vol. 87; pp. 269 - 284 |
|---|---|
| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Ltd
01.03.2019
|
| Subjects: | |
| ISSN: | 0031-3203, 1873-5142 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | •We propose a VEM algorithm for the inference of the generalized Gamma mixture model (GMM) with all the closed-form update equations.•The help function is used to approximate the lower bound of the variational objective function in GMM.•With the proposed VEM algorithm, the effective number of components as well as all the other underlying parameters in GMM can be estimated automatically and simultaneously.•The results reveal that the proposed inference method is more efficient than the standard EM algorithm.•The experimental results show that the GMM is more appropriate for the asymmetric and heavy-tailed data than Gaussian mixture model.
In this paper, we propose a Bayesian inference method for the generalized Gamma mixture model (GΓMM) based on variational expectation-maximization algorithm. Specifically, the shape parameters, the inverse scale parameters, and the mixing coefficients in the GΓMM are treated as random variables, while the power parameters are left as parameters without assigning prior distributions. The help function is designed to approximate the lower bound of the variational objective function, which facilitates the assignment of the conjugate prior distributions and leads to the closed-form update equations. On this basis, the variational E-step and the variational M-step are alternatively implemented to infer the posteriors of the variables and estimate the parameters. The computational demand is reduced by the proposed method. More importantly, the effective number of components of the GΓMM can be determined automatically. The experimental results demonstrate the effectiveness of the proposed method especially in modeling the asymmetric and heavy-tailed data. |
|---|---|
| AbstractList | •We propose a VEM algorithm for the inference of the generalized Gamma mixture model (GMM) with all the closed-form update equations.•The help function is used to approximate the lower bound of the variational objective function in GMM.•With the proposed VEM algorithm, the effective number of components as well as all the other underlying parameters in GMM can be estimated automatically and simultaneously.•The results reveal that the proposed inference method is more efficient than the standard EM algorithm.•The experimental results show that the GMM is more appropriate for the asymmetric and heavy-tailed data than Gaussian mixture model.
In this paper, we propose a Bayesian inference method for the generalized Gamma mixture model (GΓMM) based on variational expectation-maximization algorithm. Specifically, the shape parameters, the inverse scale parameters, and the mixing coefficients in the GΓMM are treated as random variables, while the power parameters are left as parameters without assigning prior distributions. The help function is designed to approximate the lower bound of the variational objective function, which facilitates the assignment of the conjugate prior distributions and leads to the closed-form update equations. On this basis, the variational E-step and the variational M-step are alternatively implemented to infer the posteriors of the variables and estimate the parameters. The computational demand is reduced by the proposed method. More importantly, the effective number of components of the GΓMM can be determined automatically. The experimental results demonstrate the effectiveness of the proposed method especially in modeling the asymmetric and heavy-tailed data. |
| Author | Li, Heng-Chao Liu, Chi Emery, William J. Datcu, Mihai Zhang, Fan Fu, Kun |
| Author_xml | – sequence: 1 givenname: Chi surname: Liu fullname: Liu, Chi organization: Sichuan Provincial Key Laboratory of Information Coding and Transmission, Southwest Jiaotong University, Chengdu 610031, China – sequence: 2 givenname: Heng-Chao orcidid: 0000-0002-9735-570X surname: Li fullname: Li, Heng-Chao email: lihengchao_78@163.com organization: Sichuan Provincial Key Laboratory of Information Coding and Transmission, Southwest Jiaotong University, Chengdu 610031, China – sequence: 3 givenname: Kun surname: Fu fullname: Fu, Kun organization: Key Laboratory of Spatial Information Processing and Application System Technology, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China – sequence: 4 givenname: Fan surname: Zhang fullname: Zhang, Fan organization: College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China – sequence: 5 givenname: Mihai surname: Datcu fullname: Datcu, Mihai organization: Remote Sensing Technology Institute, German Aerospace Center, Wessling 82234, Germany – sequence: 6 givenname: William J. surname: Emery fullname: Emery, William J. organization: Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, CO 80309, USA |
| BookMark | eNqFkM1KAzEUhYNUsK2-gYu8wNSbzG9dCFpqFSpuFNyFO5k7NWV-ShKL9elNW1cudHXhnPsdOGfEBl3fEWOXAiYCRHa1nmzQ6341kSCKIE1ApidsKIo8jlKRyAEbAsQiiiXEZ2zk3BpA5MEYsrc73JEz2HFy3rToTd_xvuYr6shiY76o4gtsW-St-fQflnjbV9TwEl1wwu8WrTlQ2PD5E8dm1Vvj39tzdlpj4-ji547Z6_38ZfYQLZ8Xj7PbZaRjyHxEAqUs4kqnOi3KvC7SFItSCIlVroGyrJRTKKEqaSpSyJO6kAQVZilIXQIl8Zglx1xte-cs1WpjQw-7UwLUfh21Vsd11H6dvRrWCdj1L0wbf-jhLZrmP_jmCFMotjVkldOGOk2VsaS9qnrzd8A3fKaGZg |
| CitedBy_id | crossref_primary_10_1016_j_patcog_2024_110791 crossref_primary_10_1016_j_neucom_2020_06_114 crossref_primary_10_1109_ACCESS_2025_3540971 crossref_primary_10_1016_j_ins_2021_06_034 crossref_primary_10_1016_j_tust_2025_106646 crossref_primary_10_1007_s10618_025_01131_5 crossref_primary_10_1016_j_neucom_2020_12_042 crossref_primary_10_1016_j_patcog_2020_107783 crossref_primary_10_3390_math10040589 crossref_primary_10_1016_j_ultras_2023_107103 crossref_primary_10_1016_j_patcog_2020_107641 crossref_primary_10_1016_j_patcog_2022_108658 crossref_primary_10_1016_j_patcog_2022_109129 crossref_primary_10_3233_JCM_226416 crossref_primary_10_1134_S1054661820030074 crossref_primary_10_1002_int_22721 crossref_primary_10_1109_ACCESS_2023_3272572 crossref_primary_10_1109_TGRS_2021_3131272 crossref_primary_10_1016_j_knosys_2025_114506 crossref_primary_10_3390_math8030373 crossref_primary_10_1109_TNNLS_2022_3213518 crossref_primary_10_1016_j_jvcir_2021_103148 crossref_primary_10_1016_j_ins_2024_121001 crossref_primary_10_1016_j_geoen_2023_211640 crossref_primary_10_1109_TGRS_2020_3011209 crossref_primary_10_3390_math13101605 crossref_primary_10_3390_wevj12010043 |
| Cites_doi | 10.1080/00401706.1992.10484955 10.1109/TNNLS.2012.2190298 10.1155/2012/481923 10.1016/j.patcog.2003.08.013 10.1080/01621459.1990.10474918 10.1016/j.patcog.2017.06.035 10.1109/TIP.2004.834664 10.1109/LSP.2012.2209874 10.1109/LCOMM.2005.02027 10.1109/TSP.2007.894234 10.1016/j.patcog.2012.04.031 10.1016/j.patcog.2014.04.002 10.1016/j.patcog.2012.09.024 10.1038/clpt.1993.124 10.1109/24.406571 10.1109/34.990138 10.1109/TGRS.2007.904951 10.1109/MSP.2008.929620 10.1109/LGRS.2013.2250905 10.1002/jae.3950060206 10.1109/TPAMI.2011.63 10.1023/A:1007665907178 10.1109/TMI.2011.2165342 10.1016/j.patcog.2013.09.036 10.1109/JSTSP.2011.2138675 10.1109/LSP.2004.840869 10.1016/j.patcog.2010.09.001 10.1016/j.patcog.2006.09.012 10.1109/TSP.2011.2168521 10.1016/j.patcog.2009.03.027 10.1016/j.patcog.2007.02.016 10.1214/aoms/1177704481 10.1111/j.2517-6161.1977.tb01600.x |
| ContentType | Journal Article |
| Copyright | 2018 Elsevier Ltd |
| Copyright_xml | – notice: 2018 Elsevier Ltd |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.patcog.2018.10.025 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1873-5142 |
| EndPage | 284 |
| ExternalDocumentID | 10_1016_j_patcog_2018_10_025 S0031320318303789 |
| GroupedDBID | --K --M -D8 -DT -~X .DC .~1 0R~ 123 1B1 1RT 1~. 1~5 29O 4.4 457 4G. 53G 5VS 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABBOA ABEFU ABFNM ABFRF ABHFT ABJNI ABMAC ABTAH ABXDB ABYKQ ACBEA ACDAQ ACGFO ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADJOM ADMUD ADMXK ADTZH AEBSH AECPX AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F0J F5P FD6 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q G8K GBLVA GBOLZ HLZ HVGLF HZ~ H~9 IHE J1W JJJVA KOM KZ1 LG9 LMP LY1 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SBC SDF SDG SDP SDS SES SEW SPC SPCBC SST SSV SSZ T5K TN5 UNMZH VOH WUQ XJE XPP ZMT ZY4 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c306t-e1a2283dc5c58b7f855a8b112ad7c0e66b290b0dbe915074f82e0da6502cb0e43 |
| ISICitedReferencesCount | 34 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000453338200022&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0031-3203 |
| IngestDate | Sat Nov 29 07:26:29 EST 2025 Tue Nov 18 21:14:54 EST 2025 Fri Feb 23 02:25:26 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Maximum likelihood estimation Finite mixture models Generalized Gamma distribution Extended factorized approximation Variational expectation-maximization (VEM) |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c306t-e1a2283dc5c58b7f855a8b112ad7c0e66b290b0dbe915074f82e0da6502cb0e43 |
| ORCID | 0000-0002-9735-570X |
| PageCount | 16 |
| ParticipantIDs | crossref_primary_10_1016_j_patcog_2018_10_025 crossref_citationtrail_10_1016_j_patcog_2018_10_025 elsevier_sciencedirect_doi_10_1016_j_patcog_2018_10_025 |
| PublicationCentury | 2000 |
| PublicationDate | March 2019 2019-03-00 |
| PublicationDateYYYYMMDD | 2019-03-01 |
| PublicationDate_xml | – month: 03 year: 2019 text: March 2019 |
| PublicationDecade | 2010 |
| PublicationTitle | Pattern recognition |
| PublicationYear | 2019 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Patrikar, Baker (bib0038) 2016 Figueiredo, Jain (bib0002) 2002; 24 Boyd, Vandenberghe (bib0032) 2004 Bouguila, Ziou, Vaillancourt (bib0013) 2004; 13 Zhou, Li, Ogunbona, Zhang (bib0008) 2017; 72 Zou, Li (bib0023) 2012 Parisi (bib0031) 1988 Chatzis, Kosmopoulos (bib0030) 2011; 44 Vegas-Sánchez-Ferrero, Martin-Fernandez, Sanches (bib0034) 2014 Dempster, Laird, Rubin (bib0025) 1977; 39 Zhan, Ma (bib0009) 2012; 19 Ma, Rana, Taghia, Flierl, Leijon (bib0012) 2014; 47 Bouveyron, Girard (bib0037) 2009; 42 Li, Prasad, Fowler (bib0010) 2014; 11 Ma, Leijon (bib0011) 2011; 33 Yang, Lai, Lin (bib0026) 2012; 45 Vegas-Sanchez-Ferrero, Fernandez, Palencia, Fernandez (bib0024) 2012; 2012 Bechte, Bonaiti-Pellie, Poisson, andP. R. Bechtel (bib0039) 1993; 54 Nguyen, Wu (bib0015) 2012; 31 Zeng, Cheung (bib0003) 2014; 47 Todros, Tabrikian (bib0006) 2007; 55 Jaggia (bib0018) 1991; 6 Li, Hong, Wu, Fan (bib0022) 2011; 5 Yang, Han, Wang, Tao, Tai (bib0016) 2013; 46 Shin, Chang, Kim (bib0021) 2005; 12 Jordan, Ghahramani, Jaakkola, Saul (bib0029) 1999; 37 Fan, Bouguila, Ziou (bib0014) 2012; 23 Bishop (bib0028) 2006 Kim, Kang (bib0036) 2007; 40 Yu, Sapiro (bib0007) 2011; 59 Chen, Chen, Hou (bib0004) 2004; 37 Stacy (bib0017) 1962; 33 Uso, Pla, Sotoca, Sevilla (bib0033) 2007; 45 Aalo, Piboongungon, Iskander (bib0020) 2005; 9 Tzikas, Likas, Galatsanos (bib0027) 2008; 25 Roeder (bib0041) 1990; 85 McLachlan, Peel (bib0001) 2004 Pham, Almhana (bib0019) 1995; 44 Faundez-Zanuy, Hagmüller, Kubin (bib0005) 2007; 40 Ghahramani, Jordan (bib0035) 1994 Crawford, DeGroot, Kadane, Small (bib0040) 1992; 34 Shin (10.1016/j.patcog.2018.10.025_bib0021) 2005; 12 Dempster (10.1016/j.patcog.2018.10.025_bib0025) 1977; 39 Chatzis (10.1016/j.patcog.2018.10.025_bib0030) 2011; 44 Vegas-Sánchez-Ferrero (10.1016/j.patcog.2018.10.025_bib0034) 2014 Nguyen (10.1016/j.patcog.2018.10.025_bib0015) 2012; 31 Boyd (10.1016/j.patcog.2018.10.025_bib0032) 2004 Bechte (10.1016/j.patcog.2018.10.025_bib0039) 1993; 54 Bouguila (10.1016/j.patcog.2018.10.025_bib0013) 2004; 13 Li (10.1016/j.patcog.2018.10.025_bib0022) 2011; 5 Bouveyron (10.1016/j.patcog.2018.10.025_bib0037) 2009; 42 Chen (10.1016/j.patcog.2018.10.025_bib0004) 2004; 37 Figueiredo (10.1016/j.patcog.2018.10.025_bib0002) 2002; 24 Zou (10.1016/j.patcog.2018.10.025_bib0023) 2012 Vegas-Sanchez-Ferrero (10.1016/j.patcog.2018.10.025_bib0024) 2012; 2012 Fan (10.1016/j.patcog.2018.10.025_bib0014) 2012; 23 Crawford (10.1016/j.patcog.2018.10.025_bib0040) 1992; 34 Patrikar (10.1016/j.patcog.2018.10.025_bib0038) 2016 Bishop (10.1016/j.patcog.2018.10.025_bib0028) 2006 Aalo (10.1016/j.patcog.2018.10.025_bib0020) 2005; 9 Zhan (10.1016/j.patcog.2018.10.025_bib0009) 2012; 19 Tzikas (10.1016/j.patcog.2018.10.025_bib0027) 2008; 25 Jordan (10.1016/j.patcog.2018.10.025_bib0029) 1999; 37 Uso (10.1016/j.patcog.2018.10.025_bib0033) 2007; 45 Yu (10.1016/j.patcog.2018.10.025_bib0007) 2011; 59 Li (10.1016/j.patcog.2018.10.025_bib0010) 2014; 11 Stacy (10.1016/j.patcog.2018.10.025_bib0017) 1962; 33 Parisi (10.1016/j.patcog.2018.10.025_bib0031) 1988 Roeder (10.1016/j.patcog.2018.10.025_bib0041) 1990; 85 Ghahramani (10.1016/j.patcog.2018.10.025_bib0035) 1994 Faundez-Zanuy (10.1016/j.patcog.2018.10.025_bib0005) 2007; 40 Ma (10.1016/j.patcog.2018.10.025_bib0012) 2014; 47 Yang (10.1016/j.patcog.2018.10.025_bib0026) 2012; 45 McLachlan (10.1016/j.patcog.2018.10.025_bib0001) 2004 Todros (10.1016/j.patcog.2018.10.025_bib0006) 2007; 55 Jaggia (10.1016/j.patcog.2018.10.025_bib0018) 1991; 6 Kim (10.1016/j.patcog.2018.10.025_bib0036) 2007; 40 Yang (10.1016/j.patcog.2018.10.025_bib0016) 2013; 46 Zeng (10.1016/j.patcog.2018.10.025_bib0003) 2014; 47 Pham (10.1016/j.patcog.2018.10.025_bib0019) 1995; 44 Zhou (10.1016/j.patcog.2018.10.025_bib0008) 2017; 72 Ma (10.1016/j.patcog.2018.10.025_bib0011) 2011; 33 |
| References_xml | – volume: 47 start-page: 2011 year: 2014 end-page: 2030 ident: bib0003 article-title: Learning a mixture model for clustering with the completed likelihood minimum message length criterion publication-title: Pattern Recognit. – year: 2004 ident: bib0001 article-title: Finite Mixture Models – volume: 2012 start-page: 481923(1 year: 2012 end-page: 25) ident: bib0024 article-title: A generalized Gamma mixture model for ultrasonic tissue characterization publication-title: Comput. Math. Methods Med. – year: 1988 ident: bib0031 article-title: Statistical Field Theory – volume: 45 start-page: 4158 year: 2007 end-page: 4171 ident: bib0033 article-title: Clustering-based hyperspectral band selection using information measures publication-title: IEEE Trans. Geosci. Remote Sens. – volume: 40 start-page: 1207 year: 2007 end-page: 1221 ident: bib0036 article-title: Texture classification and segmentation using wavelet packet frame and Gaussian mixture model publication-title: Pattern Recognit. – volume: 23 start-page: 762 year: 2012 end-page: 774 ident: bib0014 article-title: Variational learning for finite Dirichlet mixture models and applications publication-title: IEEE Trans. Neural Netw. Learn. Syst. – volume: 37 start-page: 1073 year: 2004 end-page: 1075 ident: bib0004 article-title: Speaker identification using hybrid Karhunen–Loeve transform and Gaussian mixture model approach publication-title: Pattern Recognit. – volume: 11 start-page: 153 year: 2014 end-page: 157 ident: bib0010 article-title: Hyperspectral image classification using Gaussian mixture models and Markov random fields publication-title: IEEE Geosci. Remote Sens. Lett. – volume: 42 start-page: 2649 year: 2009 end-page: 2658 ident: bib0037 article-title: Robust supervised classification with mixture models: learning from data with uncertain labels publication-title: Pattern Recognit. – volume: 37 start-page: 183 year: 1999 end-page: 233 ident: bib0029 article-title: An introduction to variational methods for graphical models publication-title: Mach. Learn. – start-page: 5935 year: 2012 end-page: 5938 ident: bib0023 article-title: MCMC estimation of finite generalized Gamma mixture model publication-title: Proc. IGARSS 2012 – volume: 45 start-page: 3950 year: 2012 end-page: 3961 ident: bib0026 article-title: A robust EM clustering algorithm for Gaussian mixture models publication-title: Pattern Recognit. – volume: 33 start-page: 1187 year: 1962 end-page: 1192 ident: bib0017 article-title: A generalization of the Gamma distribution publication-title: Ann. Math. Statist. – volume: 39 start-page: 1 year: 1977 end-page: 38 ident: bib0025 article-title: Maximum likelihood from incomplete data via EM algorithm publication-title: J. Royal Statist. Soc., Ser. B – start-page: 1673 year: 2016 end-page: 1677 ident: bib0038 article-title: Improving accuracy of Gaussian mixture model classifiers with additional discriminative training publication-title: 2016 International Joint Conference on Neural Networks (IJCNN) – volume: 47 start-page: 3143 year: 2014 end-page: 3157 ident: bib0012 article-title: Bayesian estimation of Dirichlet mixture model with variational inference publication-title: Pattern Recognit. – volume: 31 start-page: 103 year: 2012 end-page: 116 ident: bib0015 article-title: Robust student’s-t mixture model with spatial constraints and its application in medical image segmentation publication-title: IEEE Trans. Med. Imag. – year: 2014 ident: bib0034 article-title: A gamma mixture model for IVUS imaging – volume: 34 start-page: 441 year: 1992 end-page: 453 ident: bib0040 article-title: Modeling lake-chemistry distributions: approximate Bayesian methods for estimating a finite-mixture model publication-title: Technometrics – volume: 13 start-page: 1533 year: 2004 end-page: 1543 ident: bib0013 article-title: Unsupervised learning of a finite mixture model based on the Dirichlet distribution and its application publication-title: IEEE Trans. Image Process. – volume: 25 start-page: 131 year: 2008 end-page: 146 ident: bib0027 article-title: The variational approximation for Bayesian inference publication-title: IEEE Signal Process. Mag. – volume: 85 start-page: 617 year: 1990 end-page: 624 ident: bib0041 article-title: Density estimation with confidence sets exemplified by superclusters and voids in the galaxies publication-title: J. Am. Statist. Ass. – volume: 59 start-page: 5842 year: 2011 end-page: 5858 ident: bib0007 article-title: Statistical compressed sensing of Gaussian mixture models publication-title: IEEE Trans. Signal Process. – volume: 24 start-page: 381 year: 2002 end-page: 396 ident: bib0002 article-title: Unsupervised learning of finite mixture models publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 46 start-page: 1101 year: 2013 end-page: 1124 ident: bib0016 article-title: Multilayer graph cuts based unsupervised color-texture image segmentation using multivariate mixed student’s t-distribution and regional credibility merging publication-title: Pattern Recognit. – year: 2004 ident: bib0032 article-title: Convex Optimization – volume: 54 start-page: 134 year: 1993 end-page: 141 ident: bib0039 article-title: A population and family study n-acetyltransferase using caffeine urinary metabolites publication-title: Clin. Pharm. Therp. – volume: 33 start-page: 2160 year: 2011 end-page: 2173 ident: bib0011 article-title: Bayesian estimation of Beta mixture models with variational inference publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 40 start-page: 3027 year: 2007 end-page: 3034 ident: bib0005 article-title: Speaker identification security improvement by means of speech watermarking publication-title: Pattern Recognit. – volume: 44 start-page: 392 year: 1995 end-page: 397 ident: bib0019 article-title: The generalized Gamma distribution: its hazard rate and stress-strenght model publication-title: IEEE Trans. Rel. – year: 2006 ident: bib0028 article-title: Pattern Recognition and Machine Learning – volume: 9 start-page: 139 year: 2005 end-page: 141 ident: bib0020 article-title: Bit-error rate of binary digital modulation schemes in generalized Gamma fading channels publication-title: IEEE Commun. Lett. – volume: 19 start-page: 733 year: 2012 end-page: 736 ident: bib0009 article-title: Gaussian mixture model on tensor field for visual tracking publication-title: IEEE Signal Process. Lett. – volume: 44 start-page: 295 year: 2011 end-page: 306 ident: bib0030 article-title: A variational Bayesian methodology for hidden Markov models utilizing Student’s-t mixtures publication-title: Pattern Recognit. – volume: 12 start-page: 258 year: 2005 end-page: 261 ident: bib0021 article-title: Statistical modeling of speech signals based on generalized Gamma distribution publication-title: IEEE Signal Process. Lett. – volume: 5 start-page: 386 year: 2011 end-page: 397 ident: bib0022 article-title: On the empirical-statistical modeling of SAR images with generalized Gamma distribution publication-title: IEEE J. Sel. Topics Signal Process. – start-page: 120 year: 1994 end-page: 127 ident: bib0035 article-title: Supervised learning from incomplete data via an EM approach publication-title: Advances in Neural Information Processing Systems – volume: 72 start-page: 548 year: 2017 end-page: 562 ident: bib0008 article-title: Semantic action recognition by learning a pose lexicon publication-title: Pattern Recognit. – volume: 6 start-page: 169 year: 1991 end-page: 180 ident: bib0018 article-title: Specification tests based on the heterogeneous generalized Gamma model of duration: with an application to Kennan’s strike data publication-title: J. Appl. Econom. – volume: 55 start-page: 3645 year: 2007 end-page: 3658 ident: bib0006 article-title: Blind separation of independent sources using Gaussian mixture model publication-title: IEEE Trans. Signal Process. – volume: 34 start-page: 441 issue: 4 year: 1992 ident: 10.1016/j.patcog.2018.10.025_bib0040 article-title: Modeling lake-chemistry distributions: approximate Bayesian methods for estimating a finite-mixture model publication-title: Technometrics doi: 10.1080/00401706.1992.10484955 – volume: 23 start-page: 762 issue: 5 year: 2012 ident: 10.1016/j.patcog.2018.10.025_bib0014 article-title: Variational learning for finite Dirichlet mixture models and applications publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2012.2190298 – year: 2004 ident: 10.1016/j.patcog.2018.10.025_bib0032 – volume: 2012 start-page: 481923(1 year: 2012 ident: 10.1016/j.patcog.2018.10.025_bib0024 article-title: A generalized Gamma mixture model for ultrasonic tissue characterization publication-title: Comput. Math. Methods Med. doi: 10.1155/2012/481923 – volume: 37 start-page: 1073 issue: 5 year: 2004 ident: 10.1016/j.patcog.2018.10.025_bib0004 article-title: Speaker identification using hybrid Karhunen–Loeve transform and Gaussian mixture model approach publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2003.08.013 – volume: 85 start-page: 617 issue: 411 year: 1990 ident: 10.1016/j.patcog.2018.10.025_bib0041 article-title: Density estimation with confidence sets exemplified by superclusters and voids in the galaxies publication-title: J. Am. Statist. Ass. doi: 10.1080/01621459.1990.10474918 – volume: 72 start-page: 548 year: 2017 ident: 10.1016/j.patcog.2018.10.025_bib0008 article-title: Semantic action recognition by learning a pose lexicon publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2017.06.035 – volume: 13 start-page: 1533 issue: 11 year: 2004 ident: 10.1016/j.patcog.2018.10.025_bib0013 article-title: Unsupervised learning of a finite mixture model based on the Dirichlet distribution and its application publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2004.834664 – volume: 19 start-page: 733 issue: 11 year: 2012 ident: 10.1016/j.patcog.2018.10.025_bib0009 article-title: Gaussian mixture model on tensor field for visual tracking publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2012.2209874 – volume: 9 start-page: 139 issue: 2 year: 2005 ident: 10.1016/j.patcog.2018.10.025_bib0020 article-title: Bit-error rate of binary digital modulation schemes in generalized Gamma fading channels publication-title: IEEE Commun. Lett. doi: 10.1109/LCOMM.2005.02027 – volume: 55 start-page: 3645 issue: 7 year: 2007 ident: 10.1016/j.patcog.2018.10.025_bib0006 article-title: Blind separation of independent sources using Gaussian mixture model publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2007.894234 – year: 2004 ident: 10.1016/j.patcog.2018.10.025_bib0001 – volume: 45 start-page: 3950 issue: 11 year: 2012 ident: 10.1016/j.patcog.2018.10.025_bib0026 article-title: A robust EM clustering algorithm for Gaussian mixture models publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2012.04.031 – volume: 47 start-page: 3143 issue: 9 year: 2014 ident: 10.1016/j.patcog.2018.10.025_bib0012 article-title: Bayesian estimation of Dirichlet mixture model with variational inference publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2014.04.002 – volume: 46 start-page: 1101 issue: 4 year: 2013 ident: 10.1016/j.patcog.2018.10.025_bib0016 article-title: Multilayer graph cuts based unsupervised color-texture image segmentation using multivariate mixed student’s t-distribution and regional credibility merging publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2012.09.024 – volume: 54 start-page: 134 issue: 2 year: 1993 ident: 10.1016/j.patcog.2018.10.025_bib0039 article-title: A population and family study n-acetyltransferase using caffeine urinary metabolites publication-title: Clin. Pharm. Therp. doi: 10.1038/clpt.1993.124 – volume: 44 start-page: 392 issue: 3 year: 1995 ident: 10.1016/j.patcog.2018.10.025_bib0019 article-title: The generalized Gamma distribution: its hazard rate and stress-strenght model publication-title: IEEE Trans. Rel. doi: 10.1109/24.406571 – volume: 24 start-page: 381 issue: 3 year: 2002 ident: 10.1016/j.patcog.2018.10.025_bib0002 article-title: Unsupervised learning of finite mixture models publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.990138 – volume: 45 start-page: 4158 issue: 12 year: 2007 ident: 10.1016/j.patcog.2018.10.025_bib0033 article-title: Clustering-based hyperspectral band selection using information measures publication-title: IEEE Trans. Geosci. Remote Sens. doi: 10.1109/TGRS.2007.904951 – start-page: 1673 year: 2016 ident: 10.1016/j.patcog.2018.10.025_bib0038 article-title: Improving accuracy of Gaussian mixture model classifiers with additional discriminative training – volume: 25 start-page: 131 issue: 6 year: 2008 ident: 10.1016/j.patcog.2018.10.025_bib0027 article-title: The variational approximation for Bayesian inference publication-title: IEEE Signal Process. Mag. doi: 10.1109/MSP.2008.929620 – volume: 11 start-page: 153 issue: 1 year: 2014 ident: 10.1016/j.patcog.2018.10.025_bib0010 article-title: Hyperspectral image classification using Gaussian mixture models and Markov random fields publication-title: IEEE Geosci. Remote Sens. Lett. doi: 10.1109/LGRS.2013.2250905 – volume: 6 start-page: 169 issue: 2 year: 1991 ident: 10.1016/j.patcog.2018.10.025_bib0018 article-title: Specification tests based on the heterogeneous generalized Gamma model of duration: with an application to Kennan’s strike data publication-title: J. Appl. Econom. doi: 10.1002/jae.3950060206 – volume: 33 start-page: 2160 issue: 11 year: 2011 ident: 10.1016/j.patcog.2018.10.025_bib0011 article-title: Bayesian estimation of Beta mixture models with variational inference publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2011.63 – volume: 37 start-page: 183 issue: 2 year: 1999 ident: 10.1016/j.patcog.2018.10.025_bib0029 article-title: An introduction to variational methods for graphical models publication-title: Mach. Learn. doi: 10.1023/A:1007665907178 – volume: 31 start-page: 103 issue: 1 year: 2012 ident: 10.1016/j.patcog.2018.10.025_bib0015 article-title: Robust student’s-t mixture model with spatial constraints and its application in medical image segmentation publication-title: IEEE Trans. Med. Imag. doi: 10.1109/TMI.2011.2165342 – volume: 47 start-page: 2011 issue: 5 year: 2014 ident: 10.1016/j.patcog.2018.10.025_bib0003 article-title: Learning a mixture model for clustering with the completed likelihood minimum message length criterion publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2013.09.036 – volume: 5 start-page: 386 issue: 3 year: 2011 ident: 10.1016/j.patcog.2018.10.025_bib0022 article-title: On the empirical-statistical modeling of SAR images with generalized Gamma distribution publication-title: IEEE J. Sel. Topics Signal Process. doi: 10.1109/JSTSP.2011.2138675 – volume: 12 start-page: 258 issue: 3 year: 2005 ident: 10.1016/j.patcog.2018.10.025_bib0021 article-title: Statistical modeling of speech signals based on generalized Gamma distribution publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2004.840869 – volume: 44 start-page: 295 issue: 2 year: 2011 ident: 10.1016/j.patcog.2018.10.025_bib0030 article-title: A variational Bayesian methodology for hidden Markov models utilizing Student’s-t mixtures publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2010.09.001 – year: 2014 ident: 10.1016/j.patcog.2018.10.025_bib0034 – year: 2006 ident: 10.1016/j.patcog.2018.10.025_bib0028 – volume: 40 start-page: 1207 issue: 4 year: 2007 ident: 10.1016/j.patcog.2018.10.025_bib0036 article-title: Texture classification and segmentation using wavelet packet frame and Gaussian mixture model publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2006.09.012 – volume: 59 start-page: 5842 issue: 12 year: 2011 ident: 10.1016/j.patcog.2018.10.025_bib0007 article-title: Statistical compressed sensing of Gaussian mixture models publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2011.2168521 – start-page: 5935 year: 2012 ident: 10.1016/j.patcog.2018.10.025_bib0023 article-title: MCMC estimation of finite generalized Gamma mixture model – volume: 42 start-page: 2649 issue: 11 year: 2009 ident: 10.1016/j.patcog.2018.10.025_bib0037 article-title: Robust supervised classification with mixture models: learning from data with uncertain labels publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2009.03.027 – volume: 40 start-page: 3027 issue: 11 year: 2007 ident: 10.1016/j.patcog.2018.10.025_bib0005 article-title: Speaker identification security improvement by means of speech watermarking publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2007.02.016 – volume: 33 start-page: 1187 issue: 3 year: 1962 ident: 10.1016/j.patcog.2018.10.025_bib0017 article-title: A generalization of the Gamma distribution publication-title: Ann. Math. Statist. doi: 10.1214/aoms/1177704481 – volume: 39 start-page: 1 issue: 1 year: 1977 ident: 10.1016/j.patcog.2018.10.025_bib0025 article-title: Maximum likelihood from incomplete data via EM algorithm publication-title: J. Royal Statist. Soc., Ser. B doi: 10.1111/j.2517-6161.1977.tb01600.x – year: 1988 ident: 10.1016/j.patcog.2018.10.025_bib0031 – start-page: 120 year: 1994 ident: 10.1016/j.patcog.2018.10.025_bib0035 article-title: Supervised learning from incomplete data via an EM approach |
| SSID | ssj0017142 |
| Score | 2.4685698 |
| Snippet | •We propose a VEM algorithm for the inference of the generalized Gamma mixture model (GMM) with all the closed-form update equations.•The help function is used... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 269 |
| SubjectTerms | Extended factorized approximation Finite mixture models Generalized Gamma distribution Maximum likelihood estimation Variational expectation-maximization (VEM) |
| Title | Bayesian estimation of generalized Gamma mixture model based on variational EM algorithm |
| URI | https://dx.doi.org/10.1016/j.patcog.2018.10.025 |
| Volume | 87 |
| WOSCitedRecordID | wos000453338200022&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-5142 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0017142 issn: 0031-3203 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3JbtswECVap4de2nRD0w089GYokCXKpI5p4DRdEuSQAr4J3OQoiCTDsQO3X9_hJitNkSaHXgSDIOllnmfekLMg9LFUGki2ObkXUkVExaAHhSIRV3msCdF0LIVtNkGPj9l0mp_40KFL206ANg1br_P5fxU1jIGwTersPcTdbQoD8BqEDk8QOzzvJPhP_Ke2mZGmfkbdMcKZqy9d_QKG-ZnXNR_W1dpeH9hmOENjzpS5OrgC7zmcEE6Ohvxi1i6q5Vndp7EntiqnyYTx4Ueby_zv1cpd41ebEWffmlm0f8bbDjF23rdVt7I7uz7wiPWHESb_KURjBQWbjqI0idO-gvUW1WtI15nFG9vE9Ye7ocfdkcL57hzsUTszEXhs1wThuSTp62Wz_zBnXZBhiF87L9wuhdkFhgrY5SHaSij4UgO0tfdlMv3aXTzREXEF5v33CNmWNiTw5qf5O5vpMZTTbfTEuxZ4z0HiGXqgm-foaWjbgb0Wf4GmASF4gxDclriHEGwRgj1CsEUItgjBMLeHEDw5wh1CXqIfB5PT_cPIN9iIJHiKy0iPuKl-pGQmMyZoybKMMwEMnCsqYz0eiySPRayEzo3fQEqW6FhxIPWJFPBXTl-hQdM2-jXCMJLQkgiSjlOSMS0SQZnSJeeGUopsB6Xhhyqkrz5vmqBcFLeJaQdF3aq5q77yj_k0yKDwDNIxwwKAdevKN_d8p7fo8Qb_79BguVjp9-iRvFpWl4sPHlW_ASGxlVk |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Bayesian+estimation+of+generalized+Gamma+mixture+model+based+on+variational+EM+algorithm&rft.jtitle=Pattern+recognition&rft.au=Liu%2C+Chi&rft.au=Li%2C+Heng-Chao&rft.au=Fu%2C+Kun&rft.au=Zhang%2C+Fan&rft.date=2019-03-01&rft.issn=0031-3203&rft.volume=87&rft.spage=269&rft.epage=284&rft_id=info:doi/10.1016%2Fj.patcog.2018.10.025&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_patcog_2018_10_025 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0031-3203&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0031-3203&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0031-3203&client=summon |