{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:58Z","timestamp":1760242798845,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2016,11,23]],"date-time":"2016-11-23T00:00:00Z","timestamp":1479859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The performance of signal processing systems based on vector quantization depends on codebook design. In the image compression scenario, the quality of the reconstructed images depends on the codebooks used. In this paper, alternatives are proposed for accelerating families of fuzzy K-means algorithms for codebook design. The acceleration is obtained by reducing the number of iterations of the algorithms and applying efficient nearest neighbor search techniques. Simulation results concerning image vector quantization have shown that the acceleration obtained so far does not decrease the quality of the reconstructed images. Codebook design time savings up to about 40% are obtained by the accelerated versions with respect to the original versions of the algorithms.<\/jats:p>","DOI":"10.3390\/s16111963","type":"journal-article","created":{"date-parts":[[2016,11,23]],"date-time":"2016-11-23T11:12:14Z","timestamp":1479899534000},"page":"1963","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Accelerating Families of Fuzzy K-Means Algorithms for Vector Quantization Codebook Design"],"prefix":"10.3390","volume":"16","author":[{"given":"Edson","family":"Mata","sequence":"first","affiliation":[{"name":"Center of Science and Technology, Catholic University of Pernambuco (UNICAP), Recife 50050-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Silvio","family":"Bandeira","sequence":"additional","affiliation":[{"name":"Center of Science and Technology, Catholic University of Pernambuco (UNICAP), Recife 50050-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paulo","family":"De Mattos Neto","sequence":"additional","affiliation":[{"name":"Centro de Inform\u00e1tica, Universidade Federal de Pernambuco (UFPE), Recife 50740-560, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Waslon","family":"Lopes","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Center of Alternative and Renewable Energy, Federal University of Para\u00edba (UFPB), Jo\u00e3o Pessoa 58038-130, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco","family":"Madeiro","sequence":"additional","affiliation":[{"name":"Center of Science and Technology, Catholic University of Pernambuco (UNICAP), Recife 50050-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gersho, A., and Gray, R.M. (1992). Vector Quantization and Signal Compression, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4615-3626-0"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/MASSP.1984.1162229","article-title":"Vector Quantization","volume":"1","author":"Gray","year":"1984","journal-title":"IEEE ASSP Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.sigpro.2015.02.015","article-title":"Line Spectral Frequencies Modeling by a Mixture of Von Mises-Fisher Distributions","volume":"114","author":"Ma","year":"2015","journal-title":"Signal Proc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/89.221363","article-title":"Efficient Vector Quantization of LPC Parameters at 24 Bits\/Frame","volume":"1","author":"Paliwal","year":"1993","journal-title":"IEEE Trans. Audio Speech Lang. Proc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1109\/TASL.2006.885937","article-title":"Multiple-Description Predictive-Vector Quantization with Applications to Low Bit-Rate Speech Coding Over Networks","volume":"15","author":"Yahampath","year":"2007","journal-title":"IEEE Trans. Audio Speech Lang. Proc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1109\/TIP.2011.2164419","article-title":"Multiple Descriptions Coinciding Lattice Vector Quantizer for Wavelet Image Coding","volume":"21","author":"Akhtarkavan","year":"2012","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.1016\/j.engappai.2011.09.014","article-title":"Fuzzy Vector Quantization for Image Compression Based on Competitive Agglomeration and a Novel Codeword Migration Strategy","volume":"25","author":"Tsolakis","year":"2012","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.optcom.2014.02.016","article-title":"FIVQ Algorithm for Interference Hyper-Spectral Image Compression","volume":"322","author":"Wen","year":"2014","journal-title":"Opt. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2432","DOI":"10.1016\/j.sigpro.2013.03.034","article-title":"Efficient VQ-Based Image Coding Scheme Using Inverse Function and Lossless Index Coding","volume":"93","author":"Hu","year":"2013","journal-title":"Signal Proc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.compeleceng.2012.09.014","article-title":"Investigation of the Effect of Data Duration and Speaker Gender on Text-Independent Speaker Recognition","volume":"39","author":"Ertas","year":"2013","journal-title":"Comput. Electr. Eng."},{"key":"ref_11","unstructured":"Aguiar, M.A.M., and Madeiro, F. (2007). Em-TOM-A\u00e7\u00e3o: A Pros\u00f3dia em Perspectiva, Editora Universit\u00e1ria da UFPE. [1st ed.]."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1109\/TIP.2013.2260760","article-title":"A Novel Joint Data-Hiding and Compression Scheme Based on SMVQ and Image Inpainting","volume":"23","author":"Qin","year":"2014","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1049\/ip-vis:20050153","article-title":"Hiding Secret Data Adaptively in Vector Quantisation Index Tables","volume":"153","author":"Chang","year":"2006","journal-title":"IEEE Proc. Vis. Image Signal Proc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.sigpro.2016.05.032","article-title":"Reversible Data Hiding in VQ Index Table with Lossless Coding and Adaptive Switching Mechanism","volume":"129","author":"Qin","year":"2016","journal-title":"Signal Proc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.ins.2014.12.028","article-title":"A Reversible Compression Code Hiding Using SOC and SMVQ Indices","volume":"300","author":"Chang","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.sigpro.2014.09.021","article-title":"Reversible Data Hiding with High Payload Based on Referred Frequency for VQ Compressed Codes Index","volume":"108","author":"Tu","year":"2015","journal-title":"Signal Proc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/j.eswa.2014.09.001","article-title":"A Reversible Steganographic Scheme for VQ Indices Based on Joint Neighboring Coding","volume":"42","author":"Kieu","year":"2015","journal-title":"Exp. Syst. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.dsp.2014.04.014","article-title":"Variable-Dimensional Vector Modulation for Perceptual-Based DWT Blind Audio Watermarking with Adjustable Payload Capacity","volume":"31","author":"Hu","year":"2014","journal-title":"Digit. Signal Proc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"429","DOI":"10.5405\/jmbe.928","article-title":"Combining Entropy Measurements and Cepstral Analysis for Pathological Voice Assessment","volume":"32","author":"Vieira","year":"2012","journal-title":"J. Med. Biol. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/TCOM.1980.1094577","article-title":"An Algorithm for Vector Quantizer Design","volume":"28","author":"Linde","year":"1950","journal-title":"IEEE Trans. Commun."},{"key":"ref_21","first-page":"83","article-title":"On the Systematic Development of Fast Fuzzy Vector Quantization for Grayscale Image Compression","volume":"36","author":"Tsolakis","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_22","first-page":"33","article-title":"Suppressed Fuzzy-Soft Learning Vector Quantization for MRI Segmentation","volume":"52","author":"Hunga","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1109\/49.62823","article-title":"Neural Networks for Vector Quantization of Speech and Images","volume":"8","author":"Krishnamurthy","year":"1990","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/978-3-642-03211-0_17","article-title":"Terrain-Based Memetic Algorithms to Vector Quantization Design","volume":"Volume 236","author":"Krasnogor","year":"2009","journal-title":"Nature Inspired Cooperative Strategies for Optimization (NICSO 2008)"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1049\/el:19951031","article-title":"VQ Codebook Design Using Genetic Algorithms","volume":"31","author":"Pan","year":"1995","journal-title":"Electron. Lett."},{"key":"ref_26","first-page":"1078","article-title":"Vector Quantization Using the Firefly Algorithm for Image Compression","volume":"39","author":"Horng","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_27","first-page":"1382","article-title":"Image Vector Quantization Algorithm via Honey Bee Mating Optimization","volume":"38","author":"Horng","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1109\/91.649915","article-title":"An Integrated Approach to Fuzzy Learning Vector Quantization and Fuzzy C-Means Clustering","volume":"5","author":"Karayiannis","year":"1997","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1109\/83.413164","article-title":"Fuzzy Vector Quantization Algorithms and Their Application in Image Compression","volume":"4","author":"Karayiannis","year":"1995","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1016\/0031-3203(94)90052-3","article-title":"Fuzzy Kohonen Clustering Networks","volume":"27","author":"Tsao","year":"1994","journal-title":"Pattern Recognit."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3895","DOI":"10.1016\/j.ins.2008.05.017","article-title":"Improved Batch Fuzzy Learning Vector Quantization for Image Compression","volume":"178","author":"Tsekouras","year":"2008","journal-title":"Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.geoderma.2012.08.021","article-title":"Digital Soil Pattern Recognition in the Lower Namoi Valley Using Numerical Clustering of Gamma-Ray Spectrometry Data","volume":"192","author":"Triantafilisa","year":"2013","journal-title":"Geoderma"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"e10","DOI":"10.1016\/j.culher.2009.07.004","article-title":"Comparative Cluster Analysis to Localize Emergencies in Archaeology","volume":"10","author":"Malinverni","year":"2009","journal-title":"J. Cult. Herit."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"24595","DOI":"10.3390\/s150924595","article-title":"Integrated WiFi\/PDR\/Smartphone Using an Unscented Kalman Filter Algorithm for 3D Indoor Localization","volume":"15","author":"Chen","year":"2015","journal-title":"Sensors"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"7838","DOI":"10.3390\/s130607838","article-title":"Combination of RGB and Multispectral Imagery for Discrimination of Cabernet Sauvignon Grapevine Elements","volume":"13","author":"Montes","year":"2013","journal-title":"Sensors"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"16128","DOI":"10.3390\/s140916128","article-title":"White Blood Cell Segmentation by Color-Space-Based K-Means Clustering","volume":"14","author":"Zhang","year":"2014","journal-title":"Sensors"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"13132","DOI":"10.3390\/s150613132","article-title":"Using K-Nearest Neighbor Classification to Diagnose Abnormal Lung Sounds","volume":"15","author":"Chen","year":"2015","journal-title":"Sensors"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"28314","DOI":"10.3390\/s151128314","article-title":"The Node Deployment of Intelligent Sensor Networks Based on the Spatial Difference of Farmland Soil","volume":"15","author":"Liu","year":"2015","journal-title":"Sensors"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1016\/j.asoc.2015.05.038","article-title":"Conditional Spatial Fuzzy C-Means Clustering Algorithm for Segmentation of MRI Images","volume":"34","author":"Adhikaria","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.cmpb.2015.08.001","article-title":"Improved Fuzzy C-Means Based Particle Swarm Optimization (PSO) Initialization and Outlier Rejection with Level Set Methods for MR Brain Image Segmentation","volume":"122","author":"Mekhmoukh","year":"2015","journal-title":"Comput. Methods Prog. Biomed."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1604","DOI":"10.1016\/j.patrec.2011.06.023","article-title":"Comparison of Clustering Methods: A Case Study of Text-Independent Speaker Modeling","volume":"32","author":"Kinnunen","year":"2011","journal-title":"Pattern Recognit. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Alkhalaf, S., Alfarraj, O., and Hemeida, A.M. (2015, January 2\u20135). Fuzzy-VQ Image Compression based Hybrid PSOGSA Optimization Algorithm. Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Istanbul, Turkey.","DOI":"10.1109\/FUZZ-IEEE.2015.7337998"},{"key":"ref_43","unstructured":"Bhattacharyya, P., Mitra, A., and Chatterjee, A. (February, January 31). Vector Quantization Based Image Compression Using Generalized Improved Fuzzy Clustering. Proceedings of the International Conference on Control, Instrumentation, Energy and Communication (CIEC14), Kolkata, India."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1016\/0167-8655(92)90098-K","article-title":"Equal-Average Hyperplane Partitioning Method for Vector Quantization of Image Data","volume":"13","author":"Guan","year":"1992","journal-title":"Pattern Recognit. Lett."},{"key":"ref_45","first-page":"576","article-title":"A Fast Mean-Distance-Ordered Partial Codebook Search Algorithm for Image Vector Quantization","volume":"40","author":"Ra","year":"1993","journal-title":"IEEE Trans. Circuits Syst. II"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/97.551685","article-title":"Modified K-Means Algorithm for Vector Quantizer Design","volume":"4","author":"Lee","year":"1997","journal-title":"IEEE Signal Proc. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1109\/83.877216","article-title":"Comments on Modified K-Means Algorithm for Vector Quantizer Design","volume":"9","author":"Paliwal","year":"2000","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1109\/TCOM.1985.1096214","article-title":"An Improvement of the Minimum Distortion Enconding Algorithm for Vector Quantization","volume":"33","author":"Bei","year":"1985","journal-title":"IEEE Trans. Commun."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1016\/j.ins.2006.06.010","article-title":"Hadamard Transform Based Fast Codeword Search Algorithm for High-Dimensional VQ Enconding","volume":"177","author":"Chu","year":"2007","journal-title":"Inf. Sci."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1538","DOI":"10.1109\/TIP.2007.894256","article-title":"Fast Planar-Oriented Ripple Search Algorithm for Hyperspace VQ Codebook","volume":"16","author":"Chang","year":"2007","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image Quality Assessment: From Error Visibility to Structural Similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/83.481666","article-title":"Image Compression Using Wavelet Transform and Multiresolution Decomposition","volume":"5","author":"Averbuch","year":"1996","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_53","first-page":"4","article-title":"A Theory for Multiresolution Signal Decomposition: The Wavelet Representation","volume":"5","author":"Mallat","year":"1996","journal-title":"IEEE Trans. Pattern Anal. Mach. Int."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/11\/1963\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:27:15Z","timestamp":1760210835000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/11\/1963"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,23]]},"references-count":53,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2016,11]]}},"alternative-id":["s16111963"],"URL":"https:\/\/doi.org\/10.3390\/s16111963","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,11,23]]}}}