Elements of information theory
Elements of information theory
Machine Learning
Noise modelling and evaluating learning from examples
Artificial Intelligence
Technical note: some properties of splitting criteria
Machine Learning
General and Efficient Multisplitting of Numerical Attributes
Machine Learning
Partitioning Nominal Attributes in Decision Trees
Data Mining and Knowledge Discovery
Use of Contextual Information for Feature Ranking and Discretization
IEEE Transactions on Knowledge and Data Engineering
Machine Learning
An adaptation of Relief for attribute estimation in regression
ICML '97 Proceedings of the Fourteenth International Conference on Machine Learning
Boolean Reasoning for Feature Extraction Problems
ISMIS '97 Proceedings of the 10th International Symposium on Foundations of Intelligent Systems
On Fast and Simple Algorithms for Finding Maximal Subarrays and Applications in Learning Theory
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
On the Computational Complexity of Optimal Multisplitting
Fundamenta Informaticae - Intelligent Systems
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Only a subset of the boundary points—the segment borders—have to be taken into account in searching for the optimal multisplit of a numerical value range with respect to the most commonly used attribute evaluation functions of classification learning algorithms. Segments and their borders can be found efficiently in a linear-time preprocessing step.In this paper we expand the applicability of segment borders by showing that inspecting them alone suffices in optimizing any convex evaluation function. For strictly convex evaluation functions inspecting all segment borders is also necessary. These results are derived directly from Jensen's inequality.We also study the evaluation function Training Set Error which is not strictly convex. With that function the data can be preprocessed into an even smaller number of cut point candidates, called alternations, when striving for optimal partition. Examining all alternations also seems necessary, since—analogously to strictly convex functions—the placement of neighboring cut points affects the optimality of an alternation. We test empirically the reduction of the number of cut point candidates that can be obtained for Training Set Error on real-world data.