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Yayın VC-dimension of univariate decision trees(IEEE-INST Electrical Electronics Engineers Inc, 2015-02-25) Yıldız, Olcay TanerIn this paper, we give and prove the lower bounds of the Vapnik-Chervonenkis (VC)-dimension of the univariate decision tree hypothesis class. The VC-dimension of the univariate decision tree depends on the VC-dimension values of its subtrees and the number of inputs. Via a search algorithm that calculates the VC-dimension of univariate decision trees exhaustively, we show that our VC-dimension bounds are tight for simple trees. To verify that the VC-dimension bounds are useful, we also use them to get VC-generalization bounds for complexity control using structural risk minimization in decision trees, i.e., pruning. Our simulation results show that structural risk minimization pruning using the VC-dimension bounds finds trees that are more accurate as those pruned using cross validation.Yayın Feature extraction from discrete attributes(IEEE, 2010) Yıldız, Olcay TanerIn many pattern recognition applications, first decision trees are used due to their simplicity and easily interpretable nature. In this paper, we extract new features by combining k discrete attributes, where for each subset of size k of the attributes, we generate all orderings of values of those attributes exhaustively. We then apply the usual univariate decision tree classifier using these orderings as the new attributes. Our simulation results on 16 datasets from UCI repository [2] show that the novel decision tree classifier performs better than the proper in terms of error rate and tree complexity. The same idea can also be applied to other univariate rule learning algorithms such as C4.5Rules [7] and Ripper [3].
