Abstract
Currently experimental techniques such as gene expression analysis with microarrays result in the situation that the number of variables exceeds the number of observations by far. Then application of the standard classification methodology fails because of singularity of the covariance matrix. One of the possibilities to circumvent this problem is to use ridge estimates instead of the sample covariance matrix.
Raudys and Skurichina presented an analytic formula for the asymptotic error of the one-parametric ridge classification rule. Based on their approach we derived a new formula which is unlike that of Raudys and Skurichina also valid in the case of a singular covariance matrix. Under suitable conditions the formula allows to calculate the ridge parameter which minimizes the classification error. Simulation results are presented.
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Grüning, M., Kropf, S. (2006). A Ridge Classification Method for High-dimensional Observations. In: Spiliopoulou, M., Kruse, R., Borgelt, C., Nürnberger, A., Gaul, W. (eds) From Data and Information Analysis to Knowledge Engineering. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31314-1_84
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DOI: https://doi.org/10.1007/3-540-31314-1_84
Publisher Name: Springer, Berlin, Heidelberg
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