Abstract
We studied a number of measures that characterize the difficulty of a classification problem. We compared a set of real world problems to random combinations of points in this measurement space and found that real problems con- tain structures that are significantly different from the ran- dom sets. Distribution of problems in this space reveals that there exist at least two independent factors affecting a prob- lem's difficulty, and that they have notable joint effects. We suggest using this space to describe a classifier's domain of competence. This can guide static and dynamic selection of classifiers for specific problems as well as subproblems formed by confinement, projections, and transformations of the feature vectors.

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