Abstract
The idea, presented in this article, is based on a combination of hierarchical classifier with multiresolution representation of signals in the Daubechies wavelet bases. The paper concerns a multi-class recognition of random signals. It presents a multistage classifier with a hierarchical tree structure, based on a multiscale representation of signals in wavelet bases. Classes are hierarchically grouped in macro-classes and the established aggregation defines a decision tree. In each macro-class, the existence of deterministic pattern of signals is assumed. A global loss function with reject option is proposed for the multistage classifier and two strategies for the choice of loss function parameters are discussed. An analysis of risk is performed for a local (binary) attraction-limited minimum distance classifier for wavelet approximation of signals. This leads to proposals, relating to the upper estimate of the risk, called the guaranteed risk. Its value depends on the several parameters as the wavelet scale of signal representation, the support length of wavelet function, or the variance of the random noise in the macro-class. Finally, the guaranteed risk of the multistage classifier is derived.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Daubechies I (1992) Ten lectures on wavelets. SIAM Edition, Philadelphia
Devroye L, Györfi L, Lugosi G (1996) A probabilistic theory of pattern recognition. Springer, New York
Hasiewicz Z, Libal U (2014) Upper bound of risk of attraction-limited minimum distance classifier. In: Proc 18th National Conference on Automation (in Polish) 8–10 September, Wroclaw
Mallat S (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11(7):674–693
Webb AR, Copsey KD (2011) Statistical pattern recognition, 3rd edn. Wiley, New York
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Libal, U., Hasiewicz, Z. (2015). Wavelet Algorithm for Hierarchical Pattern Recognition. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_43
Download citation
DOI: https://doi.org/10.1007/978-3-319-13881-7_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13880-0
Online ISBN: 978-3-319-13881-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)