Bagging Combined Classifiers
Aggregated classifiers have proven to be successful in reducing misclassification error in a wide range of classification problems. One of the most popular is bagging. But often simple procedures perform comparably in specific applications. For example, linear discriminant analysis (LDA) provides efficient classifiers if the underlying class structure is linear regarding the predictors.
We suggest bagging for a combination of tree classifiers and LDA. The out-of-bag sample is used as an independent learning sample for the computation of linear discriminant functions. The corresponding discriminant variables of the bootstrap sample are used as additional predictors for a classification tree. We illustrate the proposal by a glaucoma classification with laser scanning image data. Moreover, we analyse the properties with a simulation study and benchmark data sets. In summary, our proposal has misclassification error comparable to LDA when LDA performs best and comparable to bagged trees when bagged trees perform best.
KeywordsLinear Discriminant Analysis Bootstrap Sample Classification Tree Optic Nerve Head Misclassification Error
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- Breiman, L. (1996): Out-of-bag estimation, Tech. rep., Statistics Department, University of California Berkeley, Berkeley CA 94708.Google Scholar
- LAUSEN, B., SAUERBREI, W., and SCHUMACHER, M. (1994): Classification and regression trees (CART) used for the exploration of prognostic factors measured on different scales, in Dirschedl, P. and Ostermann, R. (Eds.): Computational Statistics, Physica-Verlag, Heidelberg, 483–496.CrossRefGoogle Scholar
- Heidelberg Engineering (1997): Heidelberg Retina Tomograph: Bedie-nungsanleitung Software version 2.01., Heidelberg Engineering GmbH, Heidelberg.Google Scholar
- HOTHORN, T., PAL, I., GEFELLER, O., LAUSEN, B., MICHELSON, G., and PAULUS, D. (2002): Automated classification of optic nerve head topography images for glaucoma screening, in Studies in Classification, Data Analysis, and Knowledge Organization (to appear), Springer, Heidelberg.Google Scholar
- SWINDALE, N. V., STJEPANOVIC, G., CHIN, A., and MIKELBERG, F. S. (2000): Automated analysis of normal and glaucomatous optic nerve head to-pography images., Investigative Ophthalmology and Visual Science, Vol. 41, 7, 1730–42.Google Scholar
- CIAMPI, A. and LECHEVALLIER, Y. (2000): Constructing artificial neural net-works for censored survival data from statistical models, in Kiers, H., Rasson, J.-P., Groenen, P., and Schader, M. (Eds.): Data Analysis, Classification, and Related Methods, Springer, Heidelberg, 223–228.CrossRefGoogle Scholar