Abstract
In this work, the problem of estimating high density regions from univariate or multivariate data samples is studied. To be more precise, we estimate minimum volume sets whose probability is specified in advance. This problem arises in outlier detection and cluster analysis, and is strongly related to One-Class Support Vector Machines (SVM). In this paper we propose a new simpler method to solve this problem. We show its properties and introduce a new class of kernels, relating the proposed method to One-Class SVMs.
Keywords
- Class Support Vector Machine
- High Density Region
- True Mode
- Naive Algorithm
- Naive Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Alpaydin, E., Kaynak, C.: Cascading Classifiers. Kybernetika 34(4), 369–374 (1998)
Devroye, L.: Recursive estimation of the mode of a multivariate density. The Canadian Journal of Statistics 7(2), 159–167 (1979)
Devroye, L., Krzyzak, A.: On the Hilbert kernel density estimate. Statistics and Probability Letters 44, 299–308 (1999)
Moguerza, J.M., Muñoz, A.: Solving the One-Class Problem using Neighbourhood Measures. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 680–688. Springer, Heidelberg (2004)
Moguerza, J.M., Muñoz, A., Martin-Merino, M.: Detecting the Number of Clusters Using a Support Vector Machine Approach. In: Dorronsoro, J.R. (ed.) ICANN 2002. LNCS, vol. 2415, pp. 763–768. Springer, Heidelberg (2002)
Muñoz, A., Moguerza, J.M.: One-Class Support Vector Machines and density estimation: the precise relation. In: Sanfeliu, A., Martínez Trinidad, J.F., Carrasco Ochoa, J.A. (eds.) CIARP 2004. LNCS, vol. 3287, pp. 216–223. Springer, Heidelberg (2004)
Muñoz, A., Muruzabal, J.: Self-Organizing Maps for Outlier Detection. Neurocomputing 18, 33–60 (1998)
Rätsch, G., Mika, S., Schölkopf, B., Müller, K.R.: Constructing Boosting Algorithms from SVMs: an Application to One-Class Classification. IEEE Trans. on Pattern Analysis and Machine Intelligence 24(9), 1184–1199 (2002)
Schölkopf, B., Burges, C., Vapnik, V.: Extracting Support Data for a given Task. In: Proc. of the First International Conference on Knowledge Discovery and Data Mining. AAAI Press, Menlo Park (1995)
Schölkopf, B., Platt, J.C., Shawe-Taylor, J., Smola, A.J., Williamson, R.C.: Estimating the Support of a High Dimensional Distribution. Neural Computation 13(7), 1443–1471 (2001)
Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, Boca Raton (1990)
Tax, D.M.J., Duin, R.P.W.: Support Vector Domain Description. Pattern Recognition Letters 20, 1991–1999 (1999)
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Muñoz, A., Moguerza, J.M. (2005). A Naive Solution to the One-Class Problem and Its Extension to Kernel Methods. In: Sanfeliu, A., Cortés, M.L. (eds) Progress in Pattern Recognition, Image Analysis and Applications. CIARP 2005. Lecture Notes in Computer Science, vol 3773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11578079_21
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DOI: https://doi.org/10.1007/11578079_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29850-2
Online ISBN: 978-3-540-32242-9
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