Combinatorial feature selection problems

A Parameterized Complexity Analysis of Combinatorial Feature Selection Problems

“…We revisit two categories of combinatorial feature selection problems (namely dimension reduction and clustering problems) as introduced by Charikar et al [5]. Within their framework they defined (amongst others) two problems called Distinct Vectors and Hidden Clusters.…”

“…, x n|K } denotes the multiset of projections x i|K of the points in S into the dimensions in K, that is, dimensions not in K are set to zero. Distinct Vectors is NP-hard to approximate within a logarithmic factor [5]. It is also known as the Minimal Reduct problem in rough set theory [17] and was already earlier proven to be NP-hard [18].…”

“…Combinatorial feature selection [14,5] is a well-motivated alternative to the more frequently studied affine feature selection: While affine feature selection combines features to reduce dimensionality, combinatorial feature selection chooses a subspace by discarding some dimensions. The advantage of the latter is that the resulting reduced feature space is easier to interpret.…”

“…The advantage of the latter is that the resulting reduced feature space is easier to interpret. See Charikar et al [5] for a more extensive discussion in favor of combinatorial feature selection. Unfortunately, combinatorial feature selection problems are typically computationally very hard to solve (NP-hard and also hard to approximate [5]), resulting in the use of heuristic approaches in practice [2,8,12,13].…”

“…In this work, mainly following Charikar et al [5], who provided classical computational hardness results (NP-hardness and inapproximability), we adopt the fresh perspective of parameterized complexity analysis. We thus refine the known picture of the computational complexity landscape of combinatorial feature selection problems.…”