Abstract
The capacity of a clustering model can be defined as the ability to represent complex spatial data distributions. We introduce a method to quantify the capacity of an approximate spectral clustering model based on the eigenspectrum of the similarity matrix, providing the ability to measure capacity in a direct way and to estimate the most suitable model parameters. The method is tested on simple datasets and applied to a forged banknote classification problem.
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References
Buhmann, J., Tishby, N.: Empirical risk approximation a statistical learning theory of data clustering. NATO ASI Ser. Ser. F: Comput. Syst. Sci. 57–68 (1998)
Chung, F.R.K.: Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92). American Mathematical Society, Providence (1997)
De Silva, V., Tenenbaum, J.B.: Sparse multidimensional scaling using landmark points. Technical report, Stanford University (2004)
Decelle, A., Krzakala, F., Moore, C., Zdeborová, L.: Inference and phase transitions in the detection of modules in sparse networks. Phys. Rev. Lett. 107(6), 065701 (2011)
Fisher, R.A.: The use of multiple measurements in taxonomic problems. Annu. Eugen. 7(Part II), 179–188 (1936)
Gersho, A., Gray, R.M.: Vector Quantization and Signal Compression. Kluwer, Boston (1992)
Gray, R.: Vector quantization. IEEE Acoust. Speech Signal Process. Mag. 1, 4–29 (1984)
Halkidi, M., Batistakis, Y., Vazirgiannis, M.: On clustering validation techniques. J. Intell. Inf. Syst. 17(2–3), 107–145 (2001)
Handl, J., Knowles, J., Kell, D.B.: Computational cluster validation in post-genomic data analysis. Bioinformatics 21(15), 3201 (2005)
Lee, M.D.: On the complexity of additive clustering models. J. Math. Psychol. 45(1), 131–148 (2001)
Lichman, M.: UCI machine learning repository (2013). http://archive.ics.uci.edu/ml
Rose, K., Gurewitz, E., Fox, G.: Statistical mechanics and phase transitions in clustering. Phys. Rev. Lett. 65, 945–948 (1990)
Rovetta, S.: Model complexity control in clustering. In: Bassis, S., Esposito, A., Morabito, F.C., Pasero, E. (eds.) Advances in Neural Networks. SIST, vol. 54, pp. 111–120. Springer, Cham (2016). doi:10.1007/978-3-319-33747-0_11
Torgerson, W.S.: Theory and Methods of Scaling. Wiley, New York (1958)
Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)
Wigner, E.P.: Characteristic vectors of bordered matrices with infinite dimensions. Ann. Math. 62, 548–564 (1955)
Yan, D., Huang, L., Jordan, M.I.: Fast approximate spectral clustering. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 907–916. ACM (2009)
Zhou, B., Trinajstić, N.: On the largest eigenvalue of the distance matrix of a connected graph. Chem. Phys. Lett. 447(4), 384–387 (2007)
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Rovetta, S., Masulli, F., Cabri, A. (2017). Measuring Clustering Model Complexity. In: Lintas, A., Rovetta, S., Verschure, P., Villa, A. (eds) Artificial Neural Networks and Machine Learning – ICANN 2017. ICANN 2017. Lecture Notes in Computer Science(), vol 10614. Springer, Cham. https://doi.org/10.1007/978-3-319-68612-7_49
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DOI: https://doi.org/10.1007/978-3-319-68612-7_49
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