Abstract
We present an overview of association criteria that build upon the relative position of a set of reference data items with respect to given query data items, and propose fuzzy generalizations that allows to use these criteria as real-valued similarity measures. Some experimental consistency tests are also presented.
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References
Yager, R.R., Detyniecki, M., Bouchon-Meunier, B.: A context-dependent method for ordering fuzzy numbers using probabilities. Information Sciences 138(1), 237–255 (2001)
Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines (and Other Kernel-based Learning Methods). Cambridge University Press (2000)
Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007)
Zadeh, L.A.: Similarity relations and fuzzy orderings. Information Sciences 3(2), 177–200 (1971)
Ridella, S., Rovetta, S., Zunino, R.: IAVQ–interval-arithmetic vector quantization for image compression. IEEE Transactions on Circuits and Systems 47(12, Pt. II), 1378–1390 (2000)
Rovetta, S., Masulli, F.: Vector quantization and fuzzy ranks for image reconstruction. Image and Vision Computing 25(2), 204–213 (2006)
Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56(1-3), 89–113 (2004)
Fix, E., Hodges, J.L.: Discriminatory analysis. nonparametric discrimination: Consistency properties. Project Number 21-49-004 4, USAF School of Aviation Medicine, Randolph Field, Texas, USA (February 1951)
Cover, T.M., Hart, P.E.: Nearest neighbor pattern classification. IEEE Trans. Info. Theory IT-13, 21–27 (1967)
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. John Wiley and Sons, Chichester (1973)
Ridella, S., Rovetta, S., Zunino, R.: K-winner machines for pattern classification. IEEE Transactions on Neural Networks 12(2), 371–385 (2001)
Keller, J.M., Gray, M.R., Givens, J.A.: A fuzzy k-nearest neighbor algorithm. IEEE Transactions on Systems, Man and Cybernetics (4), 580–585 (1985)
Duin, R.P., Pękalska, E.: The dissimilarity space: Bridging structural and statistical pattern recognition. Pattern Recognition Letters 33(7), 826–832 (2012)
de Silva, V., Tenenbaum, J.B.: Global versus local methods in nonlinear dimensionality reduction. In: Becker, S., Thrun, S., Obermayer, K. (eds.) Proceedings NIPS, vol. 15, pp. 721–728 (2003)
Filippone, M., Masulli, F., Rovetta, S.: Clustering in the membership embedding space. International Journal of Knowledge Engineering and Soft Data Paradigms 1(4), 363–375 (2009)
Jarvis, R.A., Patrick, E.A.: Clustering using a similarity measure based on shared near neighbors. IEEE Transactions on Computers C22, 1025–1034 (1973)
Rovetta, S., Masulli, F.: Shared farthest neighbor approach to clustering of high dimensionality, low cardinality data. Pattern Recognition 39(12), 2415–2425 (2006)
Asuncion, A., Newman, D.J.: UCI machine learning repository (2007)
Fisher, R.A.: The use of multiple measurements in taxonomic problems. Annual Eugenics 7(Pt. II), 179–188 (1936)
Charytanowicz, M., Niewczas, J., Kulczycki, P., Kowalski, P.A., Łukasik, S., Żak, S.: Complete gradient clustering algorithm for features analysis of X-ray images. In: Piętka, E., Kawa, J. (eds.) Information Technologies in Biomedicine. AISC, vol. 69, pp. 15–24. Springer, Heidelberg (2010)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)
Nadler, B., Galun, M.: Fundamental limitations of spectral clustering. In: Schölkopf, B., Platt, J., Hoffman, T. (eds.) Advances in Neural Information Processing Systems 19, pp. 1017–1024. MIT Press, Cambridge (2007)
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Rovetta, S., Masulli, F., Mahmoud, H. (2013). Neighbor-Based Similarities. In: Masulli, F., Pasi, G., Yager, R. (eds) Fuzzy Logic and Applications. WILF 2013. Lecture Notes in Computer Science(), vol 8256. Springer, Cham. https://doi.org/10.1007/978-3-319-03200-9_17
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DOI: https://doi.org/10.1007/978-3-319-03200-9_17
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03199-6
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