{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T18:59:00Z","timestamp":1773514740552,"version":"3.50.1"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2020,11,4]],"date-time":"2020-11-04T00:00:00Z","timestamp":1604448000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,11,4]],"date-time":"2020-11-04T00:00:00Z","timestamp":1604448000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2021,5]]},"DOI":"10.1007\/s00034-020-01583-8","type":"journal-article","created":{"date-parts":[[2020,11,4]],"date-time":"2020-11-04T18:02:59Z","timestamp":1604512979000},"page":"2599-2607","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["The Intrinsic Dimensionality of Data"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5426-9759","authenticated-orcid":false,"given":"Subhash","family":"Kak","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,11,4]]},"reference":[{"key":"1583_CR1","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1016\/j.jmp.2009.04.005","volume":"53","author":"D Aerts","year":"2009","unstructured":"D. Aerts, Quantum structure in cognition. J. Math. Psychol. 53, 314\u2013348 (2009)","journal-title":"J. Math. Psychol."},{"key":"1583_CR2","doi-asserted-by":"publisher","first-page":"085301","DOI":"10.1088\/1751-8113\/48\/8\/085301","volume":"48","author":"JR Armstrong","year":"2015","unstructured":"J.R. Armstrong et al., Analytic solutions of topologically disjoint systems. J. Phys. A: Math. Theor. 48, 085301 (2015)","journal-title":"J. Phys. A: Math. Theor."},{"key":"1583_CR3","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1038\/533452a","volume":"533","author":"M Baker","year":"2016","unstructured":"M. Baker, 1500 scientists lift the lid on reproducibility. Nature 533, 452\u2013454 (2016)","journal-title":"Nature"},{"key":"1583_CR4","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1038\/541269a","volume":"541","author":"M Baker","year":"2017","unstructured":"M. Baker, E. Dolgin, Cancer reproducibility project releases first results. Nature 541, 269\u2013270 (2017)","journal-title":"Nature"},{"key":"1583_CR5","volume-title":"Fractals in Science","author":"A Bunde","year":"2013","unstructured":"A. Bunde, S. Havlin, Fractals in Science (Springer, Berlin, 2013)"},{"key":"1583_CR6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511997716","volume-title":"Quantum Models of Cognition and Decision","author":"JR Busemeyer","year":"2012","unstructured":"J.R. Busemeyer, P. Bruza, Quantum Models of Cognition and Decision (Cambridge University Press, Cambridge, 2012)"},{"key":"1583_CR7","volume-title":"Fractals and Fractional Calculus in Continuum Mechanics","year":"1997","unstructured":"A. Carpinteri, F. Mainardi (eds.), Fractals and Fractional Calculus in Continuum Mechanics (Springer, Wien, 1997)"},{"issue":"2","key":"1583_CR8","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1080\/00207727008920220","volume":"1","author":"RC Conant","year":"1970","unstructured":"R.C. Conant, W.R. Ashby, Every good regulator of a system must be a model of that system. Int. J. Syst. Sci. 1(2), 89\u201397 (1970)","journal-title":"Int. J. Syst. Sci."},{"key":"1583_CR9","doi-asserted-by":"publisher","DOI":"10.1002\/0470013850","volume-title":"Fractal Geometry: Mathematical Foundations and Applications","author":"KJ Falconer","year":"2003","unstructured":"K.J. Falconer, Fractal Geometry: Mathematical Foundations and Applications (Wiley, Hoboken, 2003)"},{"key":"1583_CR10","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/BF02898040","volume":"40","author":"S Kak","year":"1993","unstructured":"S. Kak, On training feedforward neural networks. Pramana 40, 35\u201342 (1993)","journal-title":"Pramana"},{"key":"1583_CR11","first-page":"79","volume":"14","author":"S Kak","year":"1999","unstructured":"S. Kak, Faster web search and prediction using instantaneously trained neural networks. IEEE Intell. Syst. 14, 79\u201382 (1999)","journal-title":"IEEE Intell. Syst."},{"key":"1583_CR12","first-page":"203","volume-title":"Biocommunication: Sign-Mediated Interactions between Cells and Organisms","author":"S Kak","year":"2016","unstructured":"S. Kak, Communication languages and agents in biological systems, in Biocommunication: Sign-Mediated Interactions between Cells and Organisms, ed. by R. Gordon, J. Seckbach (World Scientific Publishing, London, 2016), pp. 203\u2013226"},{"key":"1583_CR13","doi-asserted-by":"publisher","first-page":"3017","DOI":"10.1007\/s10773-016-2934-x","volume":"55","author":"S Kak","year":"2016","unstructured":"S. Kak, State ensembles and quantum entropy. Int. J. Theor. Phys. 55, 3017\u20133026 (2016)","journal-title":"Int. J. Theor. Phys."},{"key":"1583_CR14","doi-asserted-by":"crossref","unstructured":"S. Kak, Incomplete information and quantum decision trees. in IEEE SMC 2017, International Conference on Systems, Man, and Cybernetics. Banff, Canada (2017)","DOI":"10.1109\/SMC.2017.8122615"},{"key":"1583_CR15","unstructured":"S. Kak, Learning Based on CC1 and CC4 Neural Networks. arXiv:1712.09331 (2017)"},{"key":"1583_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/s00034-020-01480-0","author":"S Kak","year":"2020","unstructured":"S. Kak, The base-e\u00a0representation of numbers and the power law. Circuits Syst. Signal Process. (2020). https:\/\/doi.org\/10.1007\/s00034-020-01480-0","journal-title":"Circuits Syst. Signal Process."},{"key":"1583_CR17","doi-asserted-by":"crossref","unstructured":"S. Kak, Information, representation, and structure. in International Conference on Recent Trends in Mathematics and Its Applications to Graphs, Networks and Petri Nets, New Delhi, India (2020)","DOI":"10.36227\/techrxiv.12722549.v1"},{"key":"1583_CR18","unstructured":"S. Kak, Noninteger dimensional spaces and the inverse square law. (2020). TechRxiv: https:\/\/www.techrxiv.org\/articles\/preprint\/Noninteger_Dimensional_Spaces_and_the_Inverse_Square_Law\/13079720"},{"key":"1583_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-05101-2","volume-title":"Ubiquitous Quantum Structure: From Psychology to Finance","author":"AY Khrennikov","year":"2010","unstructured":"A.Y. Khrennikov, Ubiquitous Quantum Structure: From Psychology to Finance (Springer, Berlin, 2010)"},{"key":"1583_CR20","volume-title":"Theory and Application of Fractional Differential Equations","author":"AA Kilbas","year":"2006","unstructured":"A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Application of Fractional Differential Equations (Elsevier, Amsterdam, 2006)"},{"key":"1583_CR21","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1109\/TCST.2007.903094","volume":"16","author":"A Kwiatkowski","year":"2008","unstructured":"A. Kwiatkowski, H. Werner, PCA-based parameter set mappings for LPV models with fewer parameters and less overbounding. IEEE Trans. Control Syst. Technol. 16, 781\u2013788 (2008)","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"1583_CR22","doi-asserted-by":"publisher","DOI":"10.1119\/1.13295","volume-title":"The Fractal Geometry of Nature","author":"BB Mandelbrot","year":"1983","unstructured":"B.B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, New York, 1983)"},{"key":"1583_CR23","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1109\/TKDE.2003.1161582","volume":"15","author":"ER Omiecinski","year":"2003","unstructured":"E.R. Omiecinski, Alternative interest measures for mining associations in databases. IEEE Trans. Knowl. Data Eng. 15, 57\u201369 (2003)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"issue":"3","key":"1583_CR24","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1038\/scientificamerican0320-30","volume":"322","author":"R Panek","year":"2020","unstructured":"R. Panek, A cosmic crisis. Sci. Am. 322(3), 30\u201337 (2020)","journal-title":"Sci. Am."},{"key":"1583_CR25","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/j.ins.2004.02.028","volume":"171","author":"A Shortt","year":"2005","unstructured":"A. Shortt, J.G. Keating, L. Moulinier, C.N. Pannell, Optical implementation of the Kak neural network. Inf. Sci. 171, 273\u2013287 (2005)","journal-title":"Inf. Sci."},{"key":"1583_CR26","doi-asserted-by":"publisher","first-page":"1224","DOI":"10.1063\/1.523395","volume":"18","author":"FH Stillinger","year":"1977","unstructured":"F.H. Stillinger, Axiomatic basis for spaces with noninteger dimensions. J. Math. Phys. 18, 1224\u20131234 (1977)","journal-title":"J. Math. Phys."},{"key":"1583_CR27","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/s00034-002-2007-7","volume":"21","author":"KW Tang","year":"2002","unstructured":"K.W. Tang, S. Kak, Fast classification networks for signal processing. Circuits, Syst. Signal Process. 21, 207\u2013224 (2002)","journal-title":"Circuits, Syst. Signal Process."},{"key":"1583_CR28","doi-asserted-by":"publisher","first-page":"083510","DOI":"10.1063\/1.4892155","volume":"55","author":"VE Tarasov","year":"2014","unstructured":"V.E. Tarasov, Anisotropic fractal media by vector calculus in non-integer dimensional space. J. Math. Phys. 55, 083510 (2014)","journal-title":"J. Math. Phys."},{"key":"1583_CR29","first-page":"297","volume-title":"Orbifolds, in The Geometry and Topology of Three-Manifolds","author":"WP Thurston","year":"1997","unstructured":"W.P. Thurston, Orbifolds, in The Geometry and Topology of Three-Manifolds (Princeton University Press, Princeton, 1997), pp. 297\u2013355"},{"key":"1583_CR30","unstructured":"M. Verleysen, E. de Bodt, A. Lendasse, Forecasting financial time series through intrinsic dimension estimation and non-linear data projection. in Proceedings of IWANN\u201999\u2014International Work-conference on Artificial and Natural Neural Networks, Alicante (Spain), June 2\u20134, 1999, Springer, Lecture Notes in Computer Science 1607, J. Mira, Juan V. Sanchez-Andres eds. (1999)"},{"key":"1583_CR31","doi-asserted-by":"crossref","unstructured":"G.I. Webb, Discovering significant rules. in Proceedings of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data mining, KDD-2006. (pp. 434\u2013443). New York, NY: ACM (2006)","DOI":"10.1145\/1150402.1150451"},{"key":"1583_CR32","doi-asserted-by":"crossref","unstructured":"S. Wolfram, A Class of Models with the Potential to Represent Fundamental Physics. arXiv:2004.08210 (2020)","DOI":"10.25088\/ComplexSystems.29.2.107"},{"key":"1583_CR33","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s11238-010-9202-y","volume":"70","author":"VI Yukalov","year":"2010","unstructured":"V.I. Yukalov, D. Sornette, Decision theory with prospect interference and entanglement. Theor. Decis. 70, 283\u2013328 (2010)","journal-title":"Theor. Decis."},{"issue":"9","key":"1583_CR34","first-page":"842","volume":"114","author":"L Zhou","year":"2007","unstructured":"L. Zhou, Chromatic numbers of the Menger sponges. Am. Math. Mon. 114(9), 842 (2007)","journal-title":"Am. Math. Mon."},{"key":"1583_CR35","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1007\/3-540-44614-1_29","volume":"1896","author":"J Zhu","year":"2000","unstructured":"J. Zhu, G. Milne, Implementing kak neural networks on a reconfigurable computing platform. Lect. Notes Comput. Sci. 1896, 260\u2013269 (2000)","journal-title":"Lect. Notes Comput. Sci."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-020-01583-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00034-020-01583-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-020-01583-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T22:39:41Z","timestamp":1723847981000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00034-020-01583-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,4]]},"references-count":35,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["1583"],"URL":"https:\/\/doi.org\/10.1007\/s00034-020-01583-8","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,4]]},"assertion":[{"value":"29 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 October 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 November 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}