{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:27:01Z","timestamp":1760239621921,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T00:00:00Z","timestamp":1608768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["107-2118-M-009-002-MY2"],"award-info":[{"award-number":["107-2118-M-009-002-MY2"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>High-dimensional data recognition problem based on the Gaussian Mixture model has useful applications in many area, such as audio signal recognition, image analysis, and biological evolution. The expectation-maximization algorithm is a popular approach to the derivation of the maximum likelihood estimators of the Gaussian mixture model (GMM). An alternative solution is to adopt a generalized Bayes estimator for parameter estimation. In this study, an estimator based on the generalized Bayes approach is established. A simulation study shows that the proposed approach has a performance competitive to that of the conventional method in high-dimensional Gaussian mixture model recognition. We use a musical data example to illustrate this recognition problem. Suppose that we have audio data of a piece of music and know that the music is from one of four compositions, but we do not know exactly which composition it comes from. The generalized Bayes method shows a higher average recognition rate than the conventional method. This result shows that the generalized Bayes method is a competitor to the conventional method in this real application.<\/jats:p>","DOI":"10.3390\/sym13010019","type":"journal-article","created":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T22:56:45Z","timestamp":1608850605000},"page":"19","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Generalized Bayes Method for High-Dimensional Data Recognition with Applications to Audio Signal Recognition"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5863-0756","authenticated-orcid":false,"given":"Hsiuying","family":"Wang","sequence":"first","affiliation":[{"name":"Institute of Statistics, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7717","DOI":"10.1109\/ACCESS.2018.2888882","article-title":"Sound classification using convolutional neural network and tensor deep stacking network","volume":"7","author":"Khamparia","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2010\/451695","article-title":"Audio signal processing using time-frequency approaches: Coding, classification, fingerprinting, and watermarking","volume":"2010","author":"Umapathy","year":"2010","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1080\/00224065.2019.1571338","article-title":"Tolerance interval for the mixture normal distribution","volume":"52","author":"Chen","year":"2019","journal-title":"J. Qual. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1007\/s10044-014-0418-2","article-title":"SWGMM: A semi-wrapped Gaussian mixture model for clustering of circular\u2013linear data","volume":"19","author":"Roy","year":"2016","journal-title":"Pattern Anal. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"M\u00fcller, M. (2007). Information Retrieval for Music and Motion, Springer.","DOI":"10.1007\/978-3-540-74048-3"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm","volume":"39","author":"Dempster","year":"1977","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_7","unstructured":"Jang, R. (2020, December 01). Speech and Audio Processing Toolbox. Available online: http:\/\/mirlab.org\/jang\/matlab\/toolbox\/sap."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1109\/TASL.2009.2022435","article-title":"On the Use of Anti-word Models for Audio Music Annotation and Retrieval","volume":"17","author":"Chen","year":"2009","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s10618-006-0060-8","article-title":"Locally adaptive metrics for clustering high dimensional data","volume":"14","author":"Domeniconi","year":"2007","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1080\/02664763.2018.1542668","article-title":"A new look at the inverse Gaussian distribution with applications to insurance and economic data","volume":"46","author":"Punzo","year":"2019","journal-title":"J. Appl. Stat."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1111\/rssa.12009","article-title":"Bayesian Ranking Responses in Multiple Response Questions","volume":"177","author":"Wang","year":"2014","journal-title":"J. R. Stat. Soc. Ser. A (Stat. Soc.)"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Berger, J. (1985). Statistical Decision Theory and Bayesian Analysis, Springer.","DOI":"10.1007\/978-1-4757-4286-2"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1214\/15-BA973","article-title":"Asymptotic Properties of Bayes Risk of a General Class of Shrinkage Priors in Multiple Hypothesis Testing Under Sparsity","volume":"11","author":"Ghosh","year":"2016","journal-title":"Bayesian Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/89.365379","article-title":"Robust Text-Independent Speaker Identification Using Gaussian Mixture Speaker Models","volume":"3","author":"Reynolds","year":"1995","journal-title":"IEEE Trans. Speech Audio Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/j.2517-6161.1993.tb01466.x","article-title":"Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods","volume":"55","author":"Smith","year":"1993","journal-title":"J. Royal Stat. Soc. Ser. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1111\/j.2517-6161.1994.tb01985.x","article-title":"Estimation of finite mixture distributions through Bayesian sampling","volume":"56","author":"Diebolt","year":"1994","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1080\/01621459.1990.10476213","article-title":"Smith, A.F. Sampling based approaches to calculating marginal densities","volume":"85","author":"Gelfand","year":"1990","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_18","unstructured":"Robert, C. (2001). The Bayesian Choice. Springer Texts in Statistics, Springer."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1109\/TPAMI.2002.1017616","article-title":"An Efficient k-Means Clustering Algorithm: Analysis and Implementation","volume":"24","author":"Kanungo","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1214\/088342305000000016","article-title":"Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling","volume":"20","author":"Jasra","year":"2005","journal-title":"Stat. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1177\/1471082X0100100404","article-title":"Likelihood and Bayesian analysis of mixtures","volume":"1","author":"Aitkin","year":"2001","journal-title":"Stat. Model."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"McLachlan, G., and Peel, D. (2000). Finite Mixture Models, Wiley.","DOI":"10.1002\/0471721182"},{"key":"ref_23","unstructured":"Morgan, N., Bourlard, H., and Hermansky, H. (2004). Automatic Speech Recognition: An Auditory Perspective. Speech Processing in the Auditory System, Springer."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:45:43Z","timestamp":1760179543000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,24]]},"references-count":23,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010019"],"URL":"https:\/\/doi.org\/10.3390\/sym13010019","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,12,24]]}}}