# Multistage Naive Bayes Classifier with Reject Option for Multiresolution Signal Representation

### Urszula Libal

#### Abstract

In the article, two approaches to pattern recognition of signals are compared: a direct and a multistage. It is assumed that there are two generic patterns of signals, i.e. a two-class problem is considered. The direct method classifies signal in one step. The multistage method uses a multiresolution representation of signal in wavelet bases, starting from a coarse resolution at the first stage to a more detailed resolutions at the next stages. After a signal is assigned to a class, the posterior probability for this class is counted and compared with a fixed level. If the probability is higher than this level, the algorithm stops. Otherwise the signal is rejected and on the next stage the classification procedure is repeated for a higher resolution of signal. The posterior probability is calculated again. The algorithm stops when the probability is higher than a fixed level and a signal is finally assigned to a class. The wavelet filtration of signal is used for feature selection and acts as a magnifier. If the posterior probability of recognition is low on some stage, the number of features on the next stage is increased by taking a better resolution. The experiments are performed for three local decision rules: naive Bayes, linear and quadratic discriminant analysis.

#### References

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- Libal, U., (2010). Multistage classification of signals with the use of multiscale wavelet representation. In MMAR'10, 15th IEEE Int. Conference on Methods and Models in Automation and Robotics, pp.154-159.
- Libal, U., (2012). Multistage pattern recognition of signals represented in wavelet bases with reject option. In MMAR'12, 17th IEEE Int. Conference on Methods and Models in Automation and Robotics, pp.79-84.
- Mallat, S.G., (1989). A theory for multiresolution signal decomposition: the wavelet representation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 11(7), pp.674-693.
- Figure 5: Risk for naive Bayes classifier.

#### Paper Citation

#### in Harvard Style

Libal U. (2013). **Multistage Naive Bayes Classifier with Reject Option for Multiresolution Signal Representation** . In *Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,* ISBN 978-989-8565-41-9, pages 289-292. DOI: 10.5220/0004266002890292

#### in Bibtex Style

@conference{icpram13,

author={Urszula Libal},

title={Multistage Naive Bayes Classifier with Reject Option for Multiresolution Signal Representation},

booktitle={Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},

year={2013},

pages={289-292},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004266002890292},

isbn={978-989-8565-41-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,

TI - Multistage Naive Bayes Classifier with Reject Option for Multiresolution Signal Representation

SN - 978-989-8565-41-9

AU - Libal U.

PY - 2013

SP - 289

EP - 292

DO - 10.5220/0004266002890292