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Comparison of Performances of Plug-in Spatial Classification Rules
based on Bayesian and ML Estimators
Kestutis Ducinskas, Egle Zikariene and Lina Dreiziene
Department of Matematics and Statistics, Klaipeda University, Herkaus Manto str. 84, Klaipeda, Lithuania
Keywords: Bayes Rule, Spatial Discriminant Function, Gaussian Random Field, Actual Risk, Training Labels
Configuration.
Abstract: The problem of classifying a scalar Gaussian random field observation into one of two populations specified
by a different parametric drifts and common covariance model is considered. The unknown drift and scale
parameters are estimated using given a spatial training sample. This paper concerns classification
procedures associated to a parametric plug-in Bayes Rule obtained by substituting the unknown parameters
in the Bayes rule by their estimators. The Bayesian estimators are used for the particular prior distributions
of the unknown parameters. A closed-form expression is derived for the actual risk associated to the
aforementioned classification rule. An estimator of the expected risk based on the derived actual risk is used
as a performance measure for the classifier incurred by the plug-in Bayes rule. A stationary Gaussian
random field with an exponential covariance function sampled on a regular 2-dimensional lattice is used for
the simulation experiment. A critical performance comparison between the plug-in Bayes Rule defined
above and a one based on ML estimators is performed.
1 INTRODUCTION
It is known that for completely specified populations
and loss function, Bayes Rule (BR) is an optimal
classification procedure in the sense of minimum
risk (expected losses) (Anderson, 2003). When this
is not the case, the missing information is usually
provided by a training sample. For parametrically
specified populations, the training sample is used to
obtain the estimators of statistical parameters and
plugging them into the BR. The resulting
classification rule is usually called a plug-in Bayes
rule (PBR). Actual risk (ACR) or conditional risk is
usually used as a performance measure for the PBR.
Performance comparison of the PBR based on the
different types of estimators can easily be done by
the closed-form expression of the ACR.
Many authors have investigated the performance
of the PBR when the parameters are estimated from
training samples consisting of dependent
observations by using the frequentist approach for
the estimation (Kharin, 1996; Saltyte-Benth and
Ducinskas, 2005; Batsidis and Zografos, 2011). A
closed-form expression for the ACR in supervised
classification of Gaussian random field observations
is derived by Ducinskas (2009). Only the ML
estimators of the drift parameters and the scale
parameter of covariance function are considered.
In the present paper we use Bayesian estimators
instead of the ML estimators for the classification
problem described above. Proposed methodology is
useful for classification of images corrupted by the
Gaussian spatial correlated noise (Ducinskas,
Stabingiene and Stabingis, 2011).
The closed-form expression for the ACR
associated with the PBR is derived. The estimator of
expected risk is based on the derived actual risk and
is used as the performance of the PBR which is
measured by the average of the ACR usually called
an empirical estimator of expected risk.
This estimator of expected risk is a case of the
stationary Gaussian random field on 2-dimentional
regular lattice with an exponential covariance
function. The dependence of the ACR values on the
statistical hyperparameters is investigated.
Numerical comparison for the case of ML estimators
is implemented.
161
Ducinskas K., Zikariene E. and Dreiziene L..
Comparison of Performances of Plug-in Spatial Classification Rules based on Bayesian and ML Estimators.
DOI: 10.5220/0004760701610166
In Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods (ICPRAM-2014), pages 161-166
ISBN: 978-989-758-018-5
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)