Advertisement

Community Ecology

, Volume 14, Issue 2, pp 196–207 | Cite as

Compression and knowledge discovery in ecology

  • M. B. DaleEmail author
Open Access
Article

Abstract

Knowledge discovery is the non-trivial process of identifying valid, novel, interesting, potentially useful and ultimately understandable patterns in data. It encompasses a wide range of techniques ranging from data cleaning to finding manifolds and separating mixtures. Starting in the early 50’s, ecologists contributed greatly to the development of these methods and applied them to a large number of problems. However, underlying the methodology are some fundamental questions bearing on their choice and function. In addition, other fields, from sociology to quantum mechanics, have developed alternatives or solutions to various problems. In this paper, I want to look at some of the general questions underlying the processes. I shall then briefly examine aspects of 3 areas, manifolds, clustering and networks, specifically for choosing between them using the concept of compression. Finally, I shall briefly examine some of the future possibilities which remain to be examined. These provide methods of possibly improving the results of clustering analysis in vegetation studies.

Keywords

Clustering Knowledge discovery Compression Modelling Minimum message length 

References

  1. Adomavicius, G. and Tuzhilin, A. 1997. Discovery of actionable patterns in databases: the action hierarchy approach. In: Heckerman, D., Mannila, H., Pregibon, D. and Uthurusamy, R. (eds.), Proceedings 3rd International Conference Knowledge Discovery Data Mining. AAAI, pp. 111–114.Google Scholar
  2. Aerts, D. and Gabora, L. 2005. A theory of concepts and their combinations I: The structure of the sets of contexts and properties. Kybernetes 34: 151–175.CrossRefGoogle Scholar
  3. Aha, D.W., Kibler, D. and Albert, M.K. 1991. Instance-based learning algorithms. Mach. Learn. 6: 37–66.Google Scholar
  4. Aitchison, J. 1986. The Statistical Analysis of Compositional Data. Chapman & Hall, London.CrossRefGoogle Scholar
  5. Akaike, H. 1974. A new look at the statistical model identification. IEEE Trans. Autom. Control 19: 716–723.CrossRefGoogle Scholar
  6. Allen, T.F.H. and Hoekstra, T.W. 1990. The confusion between scale-defined levels and conventional levels of organization in ecology. J. Veg. Sci. 1: 5–12.CrossRefGoogle Scholar
  7. Anderson, M. Fu, G-S., Phlypo, R. and Adali, T. 2013 Independent vector analysis: identification conditions and performance bounds. arxiv 1303.7474.Google Scholar
  8. Antonelli, P.L. 1990. Applied Volterra-Hamilton systems of the Finsler type: increased species diversity as a non-chemical defense for coral against crown-of-thorns. In: Bradbury, R. H. (ed.), Acanthaster and the Coral Reef: A Theoretical Perspective, Lecture Notes in Biomathematics 8, Springer-Verlag, Berlin. pp. 220–235.CrossRefGoogle Scholar
  9. Babušaka, R., van der Venn, P.J. and Kaymak, U. 2002. Improved covariance estimation for Gustafson-Kessel clustering. Proceedings of the 2002 IEEE International Conference on Fuzzy Systems, Honolulu. pp. 1081–1085.Google Scholar
  10. Beals, E.W. 1973 Ordination: mathematical elegance and ecological naiveté. J. Ecol. 61: 23–35.CrossRefGoogle Scholar
  11. Béjar, J. 2000. Improving knowledge discovery using domain knowledge in unsupervised learning. Lect. Notes Comput. Sc. 1810: 47–54.CrossRefGoogle Scholar
  12. Benzecri, J-P. 1973. L’Analyse des Données. Vol. II. L’Analyse des Correspondances. Dunod, Paris.Google Scholar
  13. Bio, A.M.F., Alkemade, R. and Barendregt, A. 1998. Determining alternative models for vegetation response analysis: a non-parametric approach. J. Veg. Sci. 9: 5–16.CrossRefGoogle Scholar
  14. Blumer, A., Ehrenfeucht, A., Haussler, D. and Warmuth, M.K. 1987. Occam’s razor. Inform. Process. Lett. 24: 377–380.CrossRefGoogle Scholar
  15. Blumer, A., Ehrenfeucht, A., Haussler, D. and Warmuth, M.K. 1989. Learnability and the Vapnik-Chervonenkis dimension. J. ACM 36: 929–965.CrossRefGoogle Scholar
  16. Bolognini, G. and Nimis, P.L. 1993. Phytogeography of Italian deciduous oakwoods based on numerical classification of plant distribution ranges. J. Veg. Sci. 4: 847–860.CrossRefGoogle Scholar
  17. Bond, T.G. and Fox, C.M. 2007. Applying the Rasch Model: Fundamental Measurement in the Human Sciences. 2nd ed. (includes Rasch software on CD-ROM). Lawrence Erlbaum, Mahwah, NJ.Google Scholar
  18. Bonnard, C., Berry, V. and Lartillot, N. 2005. Multipolar consensus for phylogenetic trees. Syst. Biol. 55: 837–843.CrossRefGoogle Scholar
  19. Borg, I. and Groenen, P. 2005. Modern Multidimensional Scaling: Theory and Applications. 2nd ed. Springer, New York.Google Scholar
  20. Brooks, R.J. and Tobias, A.M. 1996. Choosing the best model: level of detail, complexity and model performance. Math. Comput. Model. 24: 1–14.CrossRefGoogle Scholar
  21. Buehrer, D. and Lee, C.-H. 2013 Class algebra for ontology reasoning. arXiv 1302.0334.Google Scholar
  22. Bunitine, W. and Jakulin, A. 2006. Discrete component analysis. arXiv 0604410.Google Scholar
  23. Caruana, R.R. and Freitag, D. 1994. How useful is relevance? Working Notes of the AAAI Fall Symposium on Relevance. AAAI Press, New Orleans, pp. 25–29.Google Scholar
  24. Carroll, J.D. and Chang, J.J. 1970. Analysis of individual differences in multidimensional scaling via an N-way generalization of ‘Eckhart-Young’ decomposition. Psychometrika 35: 283–319.CrossRefGoogle Scholar
  25. Cheeseman, P. 1990. On finding the most probable model. In: Sharger, J. and Langley, P. (eds.), Computational Models of Scientific Discovery and Theory Formation. Morgan Kaufmann, San Mateo, pp. 73–96.Google Scholar
  26. Chen, K. 2013. Towards the acquisition of temporal knowledge. arXiv 1304.3079.Google Scholar
  27. Cilibrasi, R. 2006. Statistical inference through data compression. ILLC Dissertation Series DS–2006–08, Institute for Logic, Language and Computation, Universiteit van Amsterdam.Google Scholar
  28. Coscia, M., Giannotti, F. and Pedrechi, D. 2012. A classification of community discovery methods in complex networks. arXiv 1206.3552.Google Scholar
  29. Coombs, C.H. and Kao, R.C. 1955. Nonmetric Factor Analysis. Engineering Research Bulletin 38, Engineering Research Institute, University of Michigan, Ann Arbor.Google Scholar
  30. Crutchfield, J.P. 1990. Information and its metric. In: Lam, L. and Morris, H.C. (eds.), Nonlinear Structures in Physical Systems — Pattern Formation, Chaos, and Waves. Springer, Berlin, pp. 119–130.CrossRefGoogle Scholar
  31. Dale, M. 1985. Graph theoretical methods for comparing phytosociological structures. Vegetatio 63: 79–88.Google Scholar
  32. Dale, M.B. 2000. On plexus representation of dissimilarities. Community Ecol. 1: 43–56.CrossRefGoogle Scholar
  33. Dale, M.B. and Anderson, D.J. 1973. Inosculate analysis of vegetation data. Austr. J. Bot. 21: 253–276.CrossRefGoogle Scholar
  34. Dale, M.B. and Barson, M.M. 1989. Grammars in vegetation analysis. Vegetatio 81: 79–94.CrossRefGoogle Scholar
  35. Dale, M.B. and Clifford, H.T. 1976. The effectiveness of higher taxonomic ranks for vegetation analysis. Austr. J. Ecol. 1: 37–62.CrossRefGoogle Scholar
  36. Dale, M.B. and Hogeweg, P. 1998. The dynamics of diversity: a cellular automaton approach. Coenoses 13: 3–15.Google Scholar
  37. Dale, P.E.R. 1983. Scale problem in classification: an application of a stochastic method to evaluate the relative heterogeneity of sample units. Austr. J. Ecol. 8: 189–198.CrossRefGoogle Scholar
  38. Day, W. H. E. 1988. Consensus methods as tools in data analysis. In: Bock, H.H. (ed.), Classification and Related Methods of Data Analysis. North Holland, Amsterdam, pp. 317–324.Google Scholar
  39. de Leeuw, J. 2005. Multidimensional Unfolding. The Encyclopedia of Statistics in Behavioral Science, Wiley, N.Y.Google Scholar
  40. Diday, E. and Bertrand, P. 1986. An extension to hierarchical clustering: the pyramidal presentation. In: Gelsema E.s. and Kanak, L.N. (eds), Pattern Recognition in Practice. Elsevier Science, Amsterdam, pp. 411–424CrossRefGoogle Scholar
  41. Diday, E., and Emilion, R. 1997. Treillis de Galois maximaux et Capacités de Choquet. Comptes Rendus de l’Académie des Sciences. Analyse Mathématique Séries 1, Mathematics. 325: 261–266.Google Scholar
  42. Echenin, M., Peltier, N. and Tourret, S. 2013. An approach to abductive reasoning in equational logic. Proceedings of the 23rd International Joint Conference on Artificial Intelligence, pp. 531–537.Google Scholar
  43. Epstein, S. 2013. All sampling methods produce outliers. arXiv 1304.3872.Google Scholar
  44. Fekete, G. and Lacza, J.Sz. 1970. A survey of plant life form systems and the respective research approaches II. Annals Historico-Naturales Musei Nationalis Hungarici Pars Botanica 62: 115–127.Google Scholar
  45. Feoli, E. and Zuccarello, V. 1986. Ordination based on classification: yet another solution? Abstracta Botanica 10: 203–219.Google Scholar
  46. Feoli, E. and Zuccarello, V. 1994. Naivete of fuzzy system space in vegetation dynamics. Coenoses 9: 25–32.Google Scholar
  47. Foster, D., Kakade, S. and Salakhutdinov, R. 2011. Domain adaptation: overfitting and small sample statistics. ArXiv 105.0857v1.Google Scholar
  48. Gell-Mann, M. 1994 The Quark and the Jaguar. W. H. Freeman, San Francisco.Google Scholar
  49. Gençay, R., Selçuk, F. and Whitcher, B. 2001. An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. Academic Press, N.Y.Google Scholar
  50. Gifi, A. 1990. Nonlinear Multivariate Analysis. Wiley, New York.Google Scholar
  51. Globerson, A. and Tisby, N. 2003 Sufficient dimensionality reduction. J. Machine Learning Res. 3: 1307–1331.Google Scholar
  52. Goodall, D.W. 1952. Objective methods in the classification of vegetation I. The use of positive interspecific correlation. Aust. J. Bot. 1: 39–63.Google Scholar
  53. Gopalakrishna, A.K., Ozcelebi, T., Liotta, A. and Lukkein, J. 2013. Relevance as a metric for evaluating machine learning algorithms. arXiv 1303.7093.Google Scholar
  54. Gorban, A., Sumner, N.R. and Zinovyev, A. 2008. Beyond the concept of manifolds: principal trees, metro maps, and elastic cubic complexes. In: Gorban, A., Kégl, B., Wunsch, D. and Zinovyev, A. (eds.), Principal Manifolds for Data Visualization and Dimension Reduction, Lecture Notes in Computational Science and Engineering 58: 219–237.Google Scholar
  55. Gower, J.C. 1977. The analysis of asymmetry and orthogonality. In: Barra, J. R. et al. (eds.), Recent Developments in Statistics. North Holland, Amsterdam, pp. 109–123.Google Scholar
  56. Grassberger, P. 1991. Information and Complexity Measures. In: Atmanspacher, H. and Scheingraber, H. (eds), Dynamical Systems, Information Dynamics, Plenum Press, New York, pp. 15–33.CrossRefGoogle Scholar
  57. Gull, S.F. 1988. Bayesian inductive inference and maximum entropy. In: Erickson, G.J. and Smith, C.R. (eds.), Maximum Entropy and Bayesian Methods in Science and Engineering. 1. Foundations. Kluwer, Dordrecht. pp. 53–74.CrossRefGoogle Scholar
  58. Gustafson, E. and Kessel, W. 1979. Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings I. E. E. E. Conference Decision Control. pp. 761 –766.Google Scholar
  59. Hájek, P. and Havránek, T. 1977. On generation of inductive hypotheses. Int. J. Man-Mach. Stud. 9: 415–438.CrossRefGoogle Scholar
  60. Heiser, W.J. 1987. Joint ordination of species and sites: the unfolding technique. In: Legendre, P. and Legendre, L. (eds.), Developments in Numerical Ecology. Springer, Berlin. pp. 189–221.CrossRefGoogle Scholar
  61. Hernández-Orallo, J. 1998. Consilience as a basis for theory formation. In: Magnani, L. Nersessian, N.J. and Thagard, P. (eds.), Proc. Conf. Model Based Reasoning, Pavia (MBR’98). Kluwer/Plenum. pp. 17–19.Google Scholar
  62. Hernández-Orallo, J. 1999. Computational measures of information gain and reinforcement in inference processes. PhD Thesis, Department of Logic and Philosophy, University of Valencia.Google Scholar
  63. Hill, M.O. 1973. Reciprocal averaging: an eigenvector method of ordination. J. Ecol. 61: 237–249.CrossRefGoogle Scholar
  64. Hill, M.O. and Gauch, H.G. Jr. 1980. Detrended correspondence analysis, an improved ordination technique. Vegetatio 42: 47–58.CrossRefGoogle Scholar
  65. Hron, K., Templ, M. and Filzmoser, P. 2010. Exploratory compositional data analysis using the R-package robCompositions. In: Aivazian, S., Filzmoser, P. and Kharin, Yu. (eds.), Proceedings 9th International Conference on Computer Data Analysis and Modeling, Belarusian State University, Minsk. 1: 179–186.Google Scholar
  66. Hubert, L., Meulman, J. and Heiser, W. 2000. Two purposes for matrix factorization: a historical appraisal. SIAM Review 42: 68–82.CrossRefGoogle Scholar
  67. Hyvärinen, A. and Oja, E. 2000. Independent component analysis: algorithms and applications. Neural Networks 13: 411–430.CrossRefPubMedGoogle Scholar
  68. Hyvärinen, A. and Pajunen, P. 1999. Nonlinear independent component analysis: existence and uniqueness results. Neural Networks 12: 429–439.CrossRefPubMedGoogle Scholar
  69. Ihm, P. and van Groenewoud, H. 1984. Correspondence analysis and Gaussian ordination. COMPSTAT lectures 3: 5–60.Google Scholar
  70. Jeffrey, H. 1961. Theory of Probability. Cambridge University Press, Cambridge.Google Scholar
  71. Jiang, J. 2008. A literature survey on domain adaptation. https://doi.org/si-faka.cs.uiuc.edu/jiang4/domain adaptation/survey/da sur-vey.pdf
  72. Joshi, M., Lingras, P., Yiyu Yao, Virendrakumar, C.B. 2010. Rough, fuzzy, interval clustering for web usage mining. In: Lingras, O., Yao, Y. Y. and Virendrakumar, C.B. (eds), 10th International Conference on Intelligent Systems Design and Applications (ISDA), pp. 397–402.Google Scholar
  73. Kadous, M.W. 1995. Expanding the scope of concept learning using meta features. School of Computer Science and Engineering, University of New South Wales. https://doi.org/rexa.info/paper/4ccb84298ff6f0a62f8263c57259cc114cb1b328
  74. Kawakami, H., Akinaga, R., Suto, H. and Katai, O. 2003. Translating novelty of business models into terms of modal logics. Proceedings 16th Australian Conference on AI, Lecture Notes in Computer Science. pp. 821–832.Google Scholar
  75. Kaymak, U. and Setnes, M. 2002. Fuzzy clustering with volume prototypes and adaptive cluster merging. IEEE Transactions on Fuzzy Systems 10(6): 705–712.CrossRefGoogle Scholar
  76. Kearns, M., Mansour, Y. and Ng, A.Y. 2013. An information analysis of hard and soft assignment methods for clustering. arXiv 1302.1552.Google Scholar
  77. Kemp, C., Perfors, A. and Tenenbaum, J.B. 2007. Learning overhypotheses with hierarchical Bayesian models. Dev. Sci. 10: 307–321.CrossRefGoogle Scholar
  78. Kiers, H.A.L. 1994. SIMPLIMAX: Oblique rotation to an optimal target with simple structure. Psychometrika 59: 567–579.CrossRefGoogle Scholar
  79. Keogh, E.J., Lonardi, S., Ratanamahatana, C.A., Wei, L., Lee, S-H. and Handley, J. 2007. Compression-based data mining of sequential data. Data Min. Knowl. Disc. 14: 99–129.CrossRefGoogle Scholar
  80. Kodratoff, Y. 1986. Leçons d’apprentissage symbolique, Editions Cépadues, Toulouse.Google Scholar
  81. Kolmogorov, A.N. 1965. Three approaches to the quantitative definition of information. Problems of Information Transmission 1: 4–17.Google Scholar
  82. Koppel, M. and Atlan, H. 1991. An almost machine-independent theory of program-length complexity, sophistication, and induction. Information Sciences 56: 23–33.CrossRefGoogle Scholar
  83. Kordon, A. 2009. Computational intelligence marketing. SIGEVO-lution 4: 2–11.CrossRefGoogle Scholar
  84. Kourie, D.G. and Oosthuizen, G.D. 1998. Lattices in machine learning: complexity issues. Acta Informatica 35: 289–292.CrossRefGoogle Scholar
  85. Krishnapuram, R. and Keller, J. 1993 A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1: 98–110.CrossRefGoogle Scholar
  86. Kruskal, J.B. 1964. Multidimensional scaling by optimizing goodness of fit to nonmetric hypothesis. Psychometrika 29: 1–27.CrossRefGoogle Scholar
  87. Kušelová, I. and Chytrý, M. 2004. Interspecific associations in phytosociological data sets: how do they change between local and regional scale? Plant Ecol. 173: 247–257.CrossRefGoogle Scholar
  88. Lambert, J.M. and Williams, W.T. 1962 Multivariate methods in plant ecology IV. Nodal Analysis. J. Ecol. 50: 775–803.CrossRefGoogle Scholar
  89. Lance, G.N. and Williams, W.T. 1967 A general theory of classificatory sorting strategies I. Hierarchical systems. Comput. J. 9: 373–380.CrossRefGoogle Scholar
  90. Laurence, S. and Margolis, E. 1999. Concepts: Core Readings. MIT Press, Cambridge.Google Scholar
  91. Lavorel, S., Mcintyre, S., Landsberg, J. and Forbes, T.D.A. 1997. Plant functional classifications: from general groups to specific groups based on disturbance. Trends Ecol. Evol. 12: 474–478.CrossRefPubMedPubMedCentralGoogle Scholar
  92. Lempel, A. and Ziv, J. 1976. On the complexity of finite sequences. IEEE Trans. Inf. Theory 22: 75–81.CrossRefGoogle Scholar
  93. Liu, B., Hsu, W., Mun, L-F. and Lee, H.-Y. 1999. Finding interesting patterns using user expectation. I.E.E.E. Transactions Knowledge Data Engineering 11: 817–832.Google Scholar
  94. Lloyd, S. 2001. Measures of complexity: A non-exhaustive list. IEEE Control Systems Magazine 21: 78.Google Scholar
  95. Lopez-Ruiz, R., Sanudo, J., Romera, E. and Calbet, X. 2012 Statistical complexity and Fisher-Shannon Information. Applications. arXiv 1201.2291.Google Scholar
  96. Lugosi, G. and Zeger, K. 1996. Concept learning using complexity regularization. IEEE Transactions Information Theory 42: 48–54.CrossRefGoogle Scholar
  97. Macnaughton-Smith, P. 1965. Some statistical and other numerical techniques for classifying individuals. Home Office Res. Unit Rep. 6, HMSO, London.Google Scholar
  98. McQuarrie, A.D.R. and Tsai, C.-L. 1998. Regression and Time Series Model Selection. World Scientific, Singapore.Google Scholar
  99. Mikkelson, G.M. 2001. Complexity and verisimilitude: realism for ecology. Biol. Philos. 16: 533–546.CrossRefGoogle Scholar
  100. Mondal, N. and Ghosh, P.P. 2013. On the existence of parallel computation in nature. arXiv 1304.0160.Google Scholar
  101. Moraczewski, I.R. 1993a. Fuzzy logic for phytosociology 1. Syntaxa as vague concepts. Vegetatio 106: 1–11.CrossRefGoogle Scholar
  102. Moraczewski, I.R. 1993b. Fuzzy logic for phytosociology 2. Generalizations and prediction. Vegetatio 106: 13–20.CrossRefGoogle Scholar
  103. Ng, A., Jordan, M. and Weiss, Y. 2001. On spectral clustering: analysis and an algorithm. Advances in Neural Information Processing Systems 14:849–856.Google Scholar
  104. Niven, B.S. 1988. The ecosystem as an algebraic category: a mathematical basis for theory of community and ecosystem in animal ecology. Coenoses 3: 83–88.Google Scholar
  105. Niven, B.S. 1992. Formalization of some basic concepts of plant ecology Coenoses 7: 103–113.Google Scholar
  106. Orlóci, L. 1991. On character-based plant community analysis: choice, arrangement, comparison. Coenoses 5: 103–108.Google Scholar
  107. Pascual-Montano, A., Crazo, J.M., Kochi, K., Lehman, D. and Pascual-Montano, R. 2006. Nonsmooth nonnegative matrix factorisation. IEEE Transactions Pattern Analysis Machine Intelligence 28: 403–415.CrossRefGoogle Scholar
  108. Pestov, V. 2010. PAC learnability of a concept class under non-atomic measures: a problem by Vidyasagar. arXiv 1006.5090.Google Scholar
  109. Pestov, V. 2011. PAC learnability versus VC dimension: a footnote to a basic result of statistical learning. arXiv 1104:2097.Google Scholar
  110. Peters, G. 2006. Some refinements of rough k-means clustering. Pattern Recognition 39: 1481–1491.CrossRefGoogle Scholar
  111. Podani, J. 1986. Comparisons of partitions in vegetation studies. Abstracta Botanica 10: 235–290.Google Scholar
  112. Podani, J. 1989. A method for generating consensus partitions and its application to community classification. Coenoses 4: 1–10.Google Scholar
  113. Podani, J. 1998. Explanatory variables in classifications and the detection of the optimum number of clusters. In: Hayashi, C., Ohsumi, N., Yajima, K., Tanaka, Y., Bock, H.-H. and Baba, Y. (eds.), Data Science, Classification and Related Methods. Springer, Tokyo, pp. 125–132.Google Scholar
  114. Porter, B.W., Bareiss, E.R. and Holte, R.C. 1990. Concept learning and heuristic classification in weak-theory domains. Artificial Intelligence 45: 229–263.CrossRefGoogle Scholar
  115. Rissanen, J. 1978. Modelling by the shortest data description. Automatica 14: 465–471.CrossRefGoogle Scholar
  116. Ruspini. E. 1970. Numerical methods for fuzzy clustering. Information Science 12: 319–350.CrossRefGoogle Scholar
  117. Ruspini, E.H. 2013. Possibility as similarity: the semantics of fuzzy logic. arXiv 1304.1115.Google Scholar
  118. Salakhutdinov, S. and Hinton, G. 2012. An efficient learning procedure for deep Boltzmann machines. Neural Comput. 24: 1967–2006.CrossRefPubMedGoogle Scholar
  119. Scholz, M. and Klinkenberg, R. 2005. An ensemble classifier for drifting concepts. In: Gama, J. and Aguilar-Ruiz, J. S. (eds.), Proceedings 2nd International Workshop on Knowledge Discovery in Data Streams, pp. 53–64.Google Scholar
  120. Schöneman, P.H. 1970. On metric multidimensional unfolding. Psychometrika 35: 349–366.CrossRefGoogle Scholar
  121. Sharger, J. and Langley, P. 1990. Computational Models of Scientific Discovery and Theory Formation. Morgan Kaufman, San Mateo.Google Scholar
  122. Shayda, D.O. 2012. Kolmogorov complexity, causality and spin. arXiv 1204.5447.Google Scholar
  123. Shi, J. and Malik, J. 2000. Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22: 888–905.CrossRefGoogle Scholar
  124. Shu, L., Chen, A., Xiong, M. and Meng, W. 2011. Efficient spectral neighborhood blocking for entity resolution. IEEE International Conference on Data Engineering (ICDE), pp. 1067–1078.Google Scholar
  125. Silberschatz, A. and Tuzhilin, A. 1996. What makes patterns interesting in knowledge discovery systems. IEEE Trans. Knowl. Data Eng. 8: 970–974.CrossRefGoogle Scholar
  126. Smith, R. L. 1985. Maximum likelihood estimation in a class of nonregular cased. Biometrika 72: 67–90.CrossRefGoogle Scholar
  127. Solomonoff, R.J. 2008. Three kinds of probabilistic induction: universal distributions and convergence theorems. Comput. J. 51: 566–570.CrossRefGoogle Scholar
  128. Sommer, S., Lauze, F. and Nielsen, M. 2010. Optimization over geodesics for exact principal geodesic analysis. arXiv 1008.1902.Google Scholar
  129. Takane, Y., Young, F.W. and de Leeuw, J. 1977. Nonmetric individual differences in multidimensional scaling: an alternating least squares method with optimal scaling features. Psychometrika 42: 7–67.CrossRefGoogle Scholar
  130. Thurstone, L.L. 1935. The Vectors of the Mind. University of Chicago Press, Chicago.Google Scholar
  131. Timm, H., Borgelt, C., Döring, C. and Kruse, R. 2009. An extension to possibilistic fuzzy cluster analysis. https://doi.org/dx.doi.org/10.1016/j.fss.2003.11.009
  132. Trunk, G. 1976. Statistical estimation of the intrinsic dimensionality of data collections. Inform. Control 12: 508–525.CrossRefGoogle Scholar
  133. Ván, P. 2006. Unique additive information measures Boltzman-Gibbs-Shannon, Fisher and beyond. Physica A 365: 28–33.CrossRefGoogle Scholar
  134. Vapnik, V.N. and Chervonenkis, A. 1971. On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its Applications 16 : 264–280.CrossRefGoogle Scholar
  135. Veness, J. Sunehag, P. and Hutter, M. 2012. On ensemble techniques for [AIXI] approximation Lecture Notes Artificial Intelligence 7716: 341–351.Google Scholar
  136. Vereshchagin, N. and Vitányi, P. 2003. Kolmogorov’s structure functions and model selection. arXiv cc/0204037v5.Google Scholar
  137. Visser, G., Dowe, D.L. and Uotila, J.P. 2009. Enhanced MML clustering using context data with climate applications. Lect. Notes Computer Sci. 5866: 170–179.CrossRefGoogle Scholar
  138. Voges, K.E. 2012. Rough clustering using an evolutionary algorithm. Proceedings 45th Hawaii International Conferences on Systems Science (HICSS), pp. 1138–1145.Google Scholar
  139. Vyugin, V.V. 1999. Most sequences are predictable. Tech. Report CLRC-TR-99-01, Computer Learning Research Centre, Royal Hollaway College, University of London, UK.Google Scholar
  140. Wallace, C.S. 1998. Intrinsic classification of spatially-correlated data. Comput. J. 41: 602–611.CrossRefGoogle Scholar
  141. Wallace, C.S. 2005. Statistical and Inductive Inference by Minimum Message Length. Springer, Berlin.Google Scholar
  142. Wallace, C.S. and Boulton, D.M. 1968. An information measure for classification. Comput. J. 11: 185–195.CrossRefGoogle Scholar
  143. Wallace, C.S. and Dale, M.B. 2005. Hierarchical clusters of vegetation types. Community Ecol. 6: 65–74.CrossRefGoogle Scholar
  144. Wang, L. and Fu, X. 2005. Data mining with computational intelligence. Advanced Information and Knowledge Processing. Springer-Verlag, New York.Google Scholar
  145. Watanabe, S. 1969. Knowing and Guessing. Wiley, New York.Google Scholar
  146. Watts, D.J. and Strogatz, S.H. 1998. Collective dynamics of “small world networks. Nature 393: 440–442.CrossRefGoogle Scholar
  147. Webb, L.J., Tracey, J.G., Williams, W.T. and Lance, G.N. 1967. Studies in the numerical analysis of complex rain-forest communities I. A comparison of methods applicable to site/species data. J. Ecol. 55: 171–191.CrossRefGoogle Scholar
  148. Werger, M.J.A. and Sprangers, J.Th.M.C. 1982. Comparison of floristic and structural classification of vegetation Vegetatio 50: 175–183.CrossRefGoogle Scholar
  149. Whewell, W. 1847. The Philosophy of the Inductive Sciences. Johnson Reprint Co., New York.Google Scholar
  150. Wille, R. 1989. Knowledge acquisition by methods of formal concept analysis. In: Diday, E. (ed.), Data Analysis, Learning Symbolic and Numerical Knowledge. Nova Science, New York - Budapest, pp. 365–380.Google Scholar
  151. Williams, W.T. and Lambert, J.M. 1959. Multivariate methods in plant ecology I. Association analysis in plant communities. J. Ecol. 47: 83–101.CrossRefGoogle Scholar
  152. Williams, W.T., Lance, G.N., Webb, L.J., Tracey, J.G. and Dale, M.B. 1969. Studies in the numerical classification of complex rain-forest communities VI. The analysis of successional data. J. Ecol. 57: 515–535.CrossRefGoogle Scholar
  153. Wittgenstein, L. 1921. Tractatus Logico-Philosophicus. Annalen der Naturphilosophie 5: 36–51.Google Scholar
  154. Wong, W., Liu, W. and Bennamon, M. 2011. Ontology learning and knowledge discovery using the web: challenges and recent advances. Information Science Reference, Hershey, PA.CrossRefGoogle Scholar
  155. Wyndham, M.P. 1985. Numerical classification of proximity data with assignment measures. J. Classif. 2: 157–172.CrossRefGoogle Scholar
  156. Wyse, N., Dubes, R. and Jain, A. K. 1980. A critical evaluation of intrinsic dimensionality algorithms. In: Gelsema, E.S. and Kanal, L.N. (eds.), Pattern Recognition in Practice. North Holland, Amsterdam, pp. 415–425.Google Scholar
  157. Yu, S. and Shi, J. 2003. Multiclass spectral clustering. Proceedings IEEE International Conference Computer Vision. pp. 313–319.Google Scholar
  158. Zadeh, L.A. 1965. Fuzzy sets. Information and Control 8: 338–353.CrossRefGoogle Scholar
  159. Zelnik-Manor, L. and Perona, P. 2005. Self-tuning spectral clustering. Advances in Neural Information Processing Systems 17: 1601–1608.Google Scholar
  160. Zhang, K. and Kwok, J.T. 2010. Clustered Nystrom method for large scale manifold learning and dimension reduction. IEEE Transactions on Neural Networks 21: 1576–1587.CrossRefGoogle Scholar
  161. Zhang, Y. and Li, T. 2011. Consensus clustering + meta clustering = multiple consensus clustering. Proceedings 24th International Florida Artificial Intelligence Research Society Conference. pp. 81–86.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest 2013

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Griffith School of EnvironmentGriffith UniversityNathanAustralia

Personalised recommendations