2007/05/18 by Rustem Takhanov, Takhanov, Rustem
Computer Science · #Advanced Graph Theory Research #Artificial Intelligence (cs.AI) #Complexity and Algorithms in Graphs #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #I.2.6 #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.0705.2765
openalex publication_date 2007/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of minimal correction of the training set to make it consistent with monotonic constraints. This problem arises during analysis of data sets via techniques that require monotone data. We show that this problem is NP-hard in general and is equivalent to finding a maximal independent set in special orgraphs. Practically important cases of that problem considered in detail. These are the cases when a partial order given on the replies set is a total order or has a dimension 2. We show that the second case can be reduced to maximization of a quadratic convex function on a convex set. For this case we construct an approximate polynomial algorithm based on convex optimization.