Abstract
This paper introduces a temporal version of Probabilistic Kernel Principal Component Analysis by using a hidden Markov model in order to obtain optimized representations of observed data through time. Recently introduced, Probabilistic Kernel Principal Component Analysis overcomes the two main disadvantages of standard Principal Component Analysis, namely, absence of probability density model and lack of high-order statistical information due to its linear structure. We extend this probabilistic approach of KPCA to mixture models in time, to enhance the capabilities of transformation and reduction of time series vectors. Results over voice disorder databases show improvements in classification accuracies even with highly reduced representations.
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References
Jolliffe, I.: Principal Component Analysis, 2nd edn. Springer, Heidelberg (2002)
Tipping, M., Bishop, C.: Probabilistic principal component analysis. Journal of the Royal Statistical Society, Series B 21(3), 611–622 (1999)
Schölkopf, B., Smola, A., Müller, K.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10(5), 1299–1319 (1998)
Tipping, M.: Sparse kernel principal component analysis. In: Press, M. (ed.) Neural Information Processing Systems, NIPS 2000, pp. 633–639 (2000)
Zhou, C.: Probabilistic analysis of kernel principal components: mixture modeling and classification. Cfar technical report, car-tr-993, University of Maryland, Department of Electrical and Computer Engineering, Maryland (2003)
Zhang, Z., Wang, G., Yeung, D., Kwok, J.: Probabilistic kernel principal component analysis. Technical report hkust-cs04-03, The Hong Kong University of Science and Technology, Department of Computer Science, Hong Kong (2004)
Schölkopf, B., Smola, A.: Learning with Kernels Support Vector Machines, Regularization, Optimization and Beyond. MIT Press, Cambridge (2002)
Härdle, W., Simar, L.: Applied Multivariate Statistical Analysis. Springer, N.Y (2003)
Rabiner, L.R.: A tutorial on hidden markov models and selected applications in speech recognition. Proceedings of The IEEE 77(2) (1989)
Alvarez, M., Henao, R.: PCA for time series classification - supplementary material. Technical report, Universidad Tecnol´ogica de Pereira, Pereira, Colombia (2006), http://ohm.utp.edu.co/~rhenao/adminsite/elements/files/kpcattsm.pdf
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Alvarez, M., Henao, R. (2006). Probabilistic Kernel Principal Component Analysis Through Time. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893028_83
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DOI: https://doi.org/10.1007/11893028_83
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46479-2
Online ISBN: 978-3-540-46480-8
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