{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T12:48:48Z","timestamp":1769690928579,"version":"3.49.0"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319912615","type":"print"},{"value":"9783319912622","type":"electronic"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-319-91262-2_39","type":"book-chapter","created":{"date-parts":[[2018,5,10]],"date-time":"2018-05-10T13:22:44Z","timestamp":1525958564000},"page":"433-444","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improvement of the Simplified Silhouette Validity Index"],"prefix":"10.1007","author":[{"given":"Artur","family":"Starczewski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krzysztof","family":"Przybyszewski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,5,11]]},"reference":[{"key":"39_CR1","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.patcog.2012.07.021","volume":"46","author":"O Arbelaitz","year":"2013","unstructured":"Arbelaitz, O., Gurrutxaga, I., Muguerza, J., Prez, J.M., Perona, I.: An extensive comparative study of cluster validity indices. Pattern Recogn. 46, 243\u2013256 (2013)","journal-title":"Pattern Recogn."},{"issue":"9","key":"39_CR2","doi-asserted-by":"publisher","first-page":"2561","DOI":"10.1109\/TPDS.2014.2357019","volume":"26","author":"J Bilski","year":"2015","unstructured":"Bilski, J., Smol\u0105g, J.: Parallel architectures for learning the RTRN and Elman dynamic neural networks. IEEE Trans. Parallel Distrib. Syst. 26(9), 2561\u20132570 (2015)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"39_CR3","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/978-3-319-39378-0_6","volume-title":"Artificial Intelligence and Soft Computing","author":"J Bilski","year":"2016","unstructured":"Bilski, J., Wilamowski, B.M.: Parallel learning of feedforward neural networks without error backpropagation. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS (LNAI), vol. 9692, pp. 57\u201369. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-39378-0_6"},{"issue":"4","key":"39_CR4","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1515\/jaiscr-2017-0019","volume":"7","author":"Guido Bologna","year":"2017","unstructured":"Bologna, G., Hayashi, Y.: Characterization of symbolic rules embedded in deep DIMLP networks: a challenge to transparency of deep learning. J. Artif. Intell. Soft Comput. Res. 7(4), 265\u2013286 (2017). https:\/\/doi.org\/10.1515\/jaiscr-2017-0019","journal-title":"Journal of Artificial Intelligence and Soft Computing Research"},{"key":"39_CR5","unstructured":"Bradley, P., Fayyad, U.: Refining initial points for k-means clustering. In: Proceedings of the Fifteenth International Conference on Knowledge Discovery and Data Mining, pp. 9\u201315. AAAI Press, New York (1998)"},{"issue":"2","key":"39_CR6","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1515\/jaiscr-2017-0009","volume":"7","author":"Oscar Chang","year":"2017","unstructured":"Chang, O., Constante, P., Gordon, A., Singana, M.: A novel deep neural network that uses space-time features for tracking and recognizing a moving object. J. Artif. Intell. Soft Comput. Res. 7(2), 125\u2013136 (2017). https:\/\/doi.org\/10.1515\/jaiscr-2017-0009","journal-title":"Journal of Artificial Intelligence and Soft Computing Research"},{"issue":"6","key":"39_CR7","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1080\/03081079.2013.798912","volume":"42","author":"K Cpa\u0142ka","year":"2013","unstructured":"Cpa\u0142ka, K., Rebrova, O., Nowicki, R., Rutkowski, L.: On design of flexible neuro-fuzzy systems for nonlinear modelling. Int. J. Gen. Syst. 42(6), 706\u2013720 (2013)","journal-title":"Int. J. Gen. Syst."},{"key":"39_CR8","unstructured":"Cpa\u0142ka, K., Rutkowski, L.: Flexible Takagi-Sugeno fuzzy systems. In: Proceedings of the 2005 IEEE International Joint Conference on Neural Networks, IJCNN (2005)"},{"issue":"3","key":"39_CR9","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1515\/jaiscr-2017-0011","volume":"7","author":"V. Susheela Devi","year":"2017","unstructured":"Devi, V.S., Meena, L.: Parallel MCNN (PMCNN) with application to prototype selection on large and streaming data. J. Artif. Intell. Soft Comput. Res. 7(3), 155\u2013169 (2017). https:\/\/doi.org\/10.1515\/jaiscr-2017-0011","journal-title":"Journal of Artificial Intelligence and Soft Computing Research"},{"issue":"9","key":"39_CR10","doi-asserted-by":"publisher","first-page":"3034","DOI":"10.1016\/j.patcog.2014.03.017","volume":"47","author":"P Fr\u00e4nti","year":"2014","unstructured":"Fr\u00e4nti, P., Rezaei, M., Zhao, Q.: Centroid index: cluster level similarity measure. Pattern Recogn. 47(9), 3034\u20133045 (2014)","journal-title":"Pattern Recogn."},{"key":"39_CR11","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1007\/978-3-319-46254-7_26","volume":"639","author":"M Gabryel","year":"2016","unstructured":"Gabryel, M.: A bag-of-features algorithm for applications using a NoSQL database. Inf. Softw. Technol. 639, 332\u2013343 (2016)","journal-title":"Inf. Softw. Technol."},{"key":"39_CR12","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1007\/978-3-319-19324-3_63","volume-title":"Artificial Intelligence and Soft Computing","author":"M Gabryel","year":"2015","unstructured":"Gabryel, M., Grycuk, R., Korytkowski, M., Holotyak, T.: Image indexing and retrieval using GSOM algorithm. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2015. LNCS (LNAI), vol. 9119, pp. 706\u2013714. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-19324-3_63"},{"key":"39_CR13","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1007\/978-3-642-38610-7_15","volume-title":"Artificial Intelligence and Soft Computing","author":"T Ga\u0142kowski","year":"2013","unstructured":"Ga\u0142kowski, T.: Kernel estimation of regression functions in the boundary regions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013. LNCS (LNAI), vol. 7895, pp. 158\u2013166. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-38610-7_15"},{"key":"39_CR14","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/978-3-319-39384-1_5","volume-title":"Artificial Intelligence and Soft Computing","author":"T Galkowski","year":"2016","unstructured":"Galkowski, T., Pawlak, M.: Nonparametric estimation of edge values of regression functions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS (LNAI), vol. 9693, pp. 49\u201359. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-39384-1_5"},{"key":"39_CR15","doi-asserted-by":"crossref","unstructured":"Hruschka, E.R., de Castro, L.N., Campello, R.J.: Evolutionary algorithms for clustering gene-expression data. In: Fourth IEEE International Conference on Data Mining, ICDM 2004, pp. 403\u2013406. IEEE (2004)","DOI":"10.1109\/ICDM.2004.10073"},{"key":"39_CR16","volume-title":"Algorithms for Clustering Data","author":"A Jain","year":"1988","unstructured":"Jain, A., Dubes, R.: Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs (1988)"},{"issue":"4","key":"39_CR17","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1515\/jaiscr-2017-0016","volume":"7","author":"Yuanzhi Ke","year":"2017","unstructured":"Ke, Y., Hagiwara, M.: An English neural network that learns texts, finds hidden knowledge, and answers questions. J. Artif. Intell. Soft Comput. Res. 7(4), 229\u2013242 (2017). https:\/\/doi.org\/10.1515\/jaiscr-2017-0016","journal-title":"Journal of Artificial Intelligence and Soft Computing Research"},{"issue":"3","key":"39_CR18","doi-asserted-by":"publisher","first-page":"782","DOI":"10.1016\/j.patcog.2009.09.018","volume":"43","author":"LF Lago-Fern\u00e1ndez","year":"2010","unstructured":"Lago-Fern\u00e1ndez, L.F., Corbacho, F.: Normality-based validation for crisp clustering. Pattern Recogn. 43(3), 782\u2013795 (2010)","journal-title":"Pattern Recogn."},{"key":"39_CR19","unstructured":"Lichman, M.: UCI Machine Learning Repository. University of California, School of Information and Computer Science, Irvine, CA (2013). http:\/\/archive.ics.uci.edu\/ml"},{"issue":"2","key":"39_CR20","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1515\/jaiscr-2017-0008","volume":"7","author":"Han Liu","year":"2017","unstructured":"Liu, H., Gegov, A., Cocea, M.: Rule based networks: an efficient and interpretable representation of computational models. J. Artif. Intell. Soft Comput. Res. 7(2), 111\u2013123 (2017). https:\/\/doi.org\/10.1515\/jaiscr-2017-0008","journal-title":"Journal of Artificial Intelligence and Soft Computing Research"},{"issue":"3","key":"39_CR21","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1111\/1467-9868.00082","volume":"59","author":"Xiao-Li Meng","year":"1997","unstructured":"Meng, X., van Dyk, D.: The EM algorithm - an old folk-song sung to a fast new tune. J. Roy. Stat. Soc. Ser. B (Methodol.) 59(3), 511\u2013567 (1997)","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"4","key":"39_CR22","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1093\/comjnl\/26.4.354","volume":"26","author":"F Murtagh","year":"1983","unstructured":"Murtagh, F.: A survey of recent advances in hierarchical clustering algorithms. Comput. J. 26(4), 354\u2013359 (1983)","journal-title":"Comput. J."},{"issue":"3","key":"39_CR23","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1109\/91.413225","volume":"3","author":"NR Pal","year":"1995","unstructured":"Pal, N.R., Bezdek, J.C.: On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Syst. 3(3), 370\u2013379 (1995)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"2","key":"39_CR24","doi-asserted-by":"publisher","first-page":"3336","DOI":"10.1016\/j.eswa.2008.01.039","volume":"36","author":"Hae-Sang Park","year":"2009","unstructured":"Park, H.S., Jun, C.H.: A simple and fast algorithm for K-medoids clustering. Expert Syst. Appl. 36(2), 3336\u20133341 (2009)","journal-title":"Expert Systems with Applications"},{"key":"39_CR25","doi-asserted-by":"crossref","unstructured":"Rohlf, F.: Single-link clustering algorithms. In: Krishnaiah, P.R, Kanal, L.N. (eds.) Handbook of Statistics, vol. 2, pp. 267\u2013284 (1982)","DOI":"10.1016\/S0169-7161(82)02015-X"},{"key":"39_CR26","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0377-0427(87)90125-7","volume":"20","author":"PJ Rousseeuw","year":"1987","unstructured":"Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53\u201365 (1987)","journal-title":"J. Comput. Appl. Math."},{"key":"39_CR27","unstructured":"Rutkowski L, Cpa\u0142ka K.: Compromise approach to neuro-fuzzy systems. In: Sincak, P., Vascak, J., Kvasnicka, V., Pospichal, J. (eds.) Intelligent Technologies - Theory and Applications. New Trends in Intelligent Technologies. Frontiers in Artificial Intelligence and Applications, vol. 76, pp. 85\u201390 (2002)"},{"issue":"2","key":"39_CR28","first-page":"297","volume":"31","author":"L Rutkowski","year":"2002","unstructured":"Rutkowski, L., Cpa\u0142ka, K.: A neuro-fuzzy controller with a compromise fuzzy reasoning. Control Cybern. 31(2), 297\u2013308 (2002)","journal-title":"Control Cybern."},{"issue":"5","key":"39_CR29","doi-asserted-by":"publisher","first-page":"1555","DOI":"10.1016\/j.asoc.2011.12.013","volume":"12","author":"S Saha","year":"2012","unstructured":"Saha, S., Bandyopadhyay, S.: Some connectivity based cluster validity indices. Appl. Soft Comput. 12(5), 1555\u20131565 (2012)","journal-title":"Appl. Soft Comput."},{"issue":"1","key":"39_CR30","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s10044-007-0099-1","volume":"12","author":"AS Sameh","year":"2009","unstructured":"Sameh, A.S., Asoke, K.N.: Development of assessment criteria for clustering algorithms. Pattern Anal. Appl. 12(1), 79\u201398 (2009)","journal-title":"Pattern Anal. Appl."},{"issue":"1","key":"39_CR31","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1515\/jaiscr-2016-0003","volume":"6","author":"Ahmed M. Serdah","year":"2016","unstructured":"Serdah, A.M., Ashour, W.M.: Clustering large-scale data based on modified affinity propagation algorithm. J. Artif. Intell. Soft Comput. Res. 6(1), 23\u201333 (2016). https:\/\/doi.org\/10.1515\/jaiscr-2016-0003","journal-title":"Journal of Artificial Intelligence and Soft Computing Research"},{"key":"39_CR32","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.asoc.2014.05.001","volume":"22","author":"H-L Shieh","year":"2014","unstructured":"Shieh, H.-L.: Robust validity index for a modified subtractive clustering algorithm. Appl. Soft Comput. 22, 47\u201359 (2014)","journal-title":"Appl. Soft Comput."},{"issue":"3","key":"39_CR33","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1007\/s10044-015-0525-8","volume":"20","author":"A Starczewski","year":"2017","unstructured":"Starczewski, A.: A new validity index for crisp clusters. Pattern Anal. Appl. 20(3), 687\u2013700 (2017)","journal-title":"Pattern Anal. Appl."},{"key":"39_CR34","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1007\/978-3-319-39384-1_10","volume-title":"Artificial Intelligence and Soft Computing","author":"A Starczewski","year":"2016","unstructured":"Starczewski, A., Krzy\u017cak, A.: A modification of the silhouette index for the improvement of cluster validity assessment. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS (LNAI), vol. 9693, pp. 114\u2013124. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-39384-1_10"},{"key":"39_CR35","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/978-3-319-59060-8_16","volume-title":"Artificial Intelligence and Soft Computing","author":"A Starczewski","year":"2017","unstructured":"Starczewski, A., Krzy\u017cak, A.: Improvement of the validity index for\u00a0determination of an appropriate data partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2017. LNCS (LNAI), vol. 10246, pp. 159\u2013170. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-59060-8_16"},{"key":"39_CR36","doi-asserted-by":"publisher","first-page":"2541","DOI":"10.1016\/j.patcog.2009.02.010","volume":"42","author":"KL Wu","year":"2009","unstructured":"Wu, K.L., Yang, M.S., Hsieh, J.N.: Robust cluster validity indexes. Pattern Recogn. 42, 2541\u20132550 (2009)","journal-title":"Pattern Recogn."},{"issue":"4","key":"39_CR37","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1002\/sam.10080","volume":"3","author":"L Vendramin","year":"2010","unstructured":"Vendramin, L., Campello, R.J., Hruschka, E.R.: Relative clustering validity criteria: a comparative overview. Stat. Anal. Data Min. 3(4), 209\u2013235 (2010)","journal-title":"Stat. Anal. Data Min."},{"key":"39_CR38","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.datak.2014.07.008","volume":"92","author":"Q Zhao","year":"2014","unstructured":"Zhao, Q., Fr\u00e4nti, P.: WB-index: a sum-of-squares based index for cluster validity. Data Knowl. Eng. 92, 77\u201389 (2014)","journal-title":"Data Knowl. Eng."}],"container-title":["Lecture Notes in Computer Science","Artificial Intelligence and Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-91262-2_39","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T12:24:57Z","timestamp":1751631897000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-91262-2_39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319912615","9783319912622"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-91262-2_39","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018]]},"assertion":[{"value":"11 May 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICAISC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Artificial Intelligence and Soft Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Zakopane","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 June 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 June 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"icaisc2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/icaisc.eu\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}