Many learning situations involve separation of labeled training instances by hyperplanes. Consistent separation is of theoretical interest, but the real goal is rather to minimize the number of errors using a bounded number of hyperplanes. Exact minimization of empirical error in a high-dimensional grid induced into the feature space by axis-parallel hyperplanes is NP-hard. We develop two approximation schemes with performance guarantees, a greedy set covering scheme for producing a consistently labeled grid, and integer programming rounding scheme for finding the minimum error grid with bounded number of hyperplanes. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Elomaa, T., Kujala, J., & Rousu, J. (2005). Approximation algorithms for minimizing empirical error by axis-parallel hyperplanes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3720 LNAI, pp. 547–555). Springer Verlag. https://doi.org/10.1007/11564096_53
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