The nature of statistical learning theory
The nature of statistical learning theory
Complexity Measures of Supervised Classification Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
An optimization criterion for generalized discriminant analysis on undersampled problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Domains of Competence of Artificial Neural Networks Using Measures of Separability of Classes
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
IEEE Transactions on Evolutionary Computation
Information Sciences: an International Journal
Linear separability and classification complexity
Expert Systems with Applications: An International Journal
Analysis of data complexity measures for classification
Expert Systems with Applications: An International Journal
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Regularized linear classifiers have been successfully applied in undersampled, i.e. small sample size/high dimensionality biomedical classification problems. Additionally, a design of data complexity measures was proposed in order to assess the competence of a classifier in a particular context. Our work was motivated by the analysis of ill-posed regression problems by Elden and the interpretation of linear discriminant analysis as a mean square error classifier. Using Singular Value Decomposition analysis, we define a discriminatory power spectrum and show that it provides useful means of data complexity assessment for undersampled classification problems. In five real-life biomedical data sets of increasing difficulty we demonstrate how the data complexity of a classification problem can be related to the performance of regularized linear classifiers. We show that the concentration of the discriminatory power manifested in the discriminatory power spectrum is a deciding factor for the success of the regularized linear classifiers in undersampled classification problems. As a practical outcome of our work, the proposed data complexity assessment may facilitate the choice of a classifier for a given undersampled problem.