Iterative column subset selection

Ordozgoiti, Bruno; Canaval, Sandra Gómez; Mozó, Alberto

doi:10.1007/s10115-017-1115-4

Cited by 11 publications

(6 citation statements)

References 30 publications

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“…This algorithm has been shown empirically to outperform other state-of-the-art methods, and an approximation bound w.r.t. S opt S + opt A 2 F has also been provided (Ordozgoiti, Canaval, and Mozo 2018).…”

Section: Related Workmentioning

confidence: 99%

Unsupervised Feature Selection by Pareto Optimization

Feng

Qian

Tang

2019

AAAI

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Dimensionality reduction is often employed to deal with the data with a huge number of features, which can be generally divided into two categories: feature transformation and feature selection. Due to the interpretability, the efficiency during inference and the abundance of unlabeled data, unsupervised feature selection has attracted much attention. In this paper, we consider its natural formulation, column subset selection (CSS), which is to minimize the reconstruction error of a data matrix by selecting a subset of features. We propose an anytime randomized iterative approach POCSS, which minimizes the reconstruction error and the number of selected features simultaneously. Its approximation guarantee is well bounded. Empirical results exhibit the superior performance of POCSS over the state-of-the-art algorithms.

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Section: Related Workmentioning

confidence: 99%

Unsupervised Feature Selection by Pareto Optimization

Feng

Qian

Tang

2019

AAAI

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“…For the ease of theoretical treatment, this minimization problem is often equivalently reformulated as a maximization problem (Bhaskara et al 2016;Ordozgoiti, Canaval, and Mozo 2018):…”

Section: Subset Selectionmentioning

confidence: 99%

Subset Selection by Pareto Optimization with Recombination

Qian

Bian

Feng

2020

AAAI

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Subset selection, i.e., to select a limited number of items optimizing some given objective function, is a fundamental problem with various applications such as unsupervised feature selection and sparse regression. By employing a multi-objective evolutionary algorithm (EA) with mutation only to optimize the given objective function and minimize the number of selected items simultaneously, the recently proposed POSS algorithm achieves state-of-the-art performance for subset selection. In this paper, we propose the PORSS algorithm by incorporating recombination, a characterizing feature of EAs, into POSS. We prove that PORSS can achieve the optimal polynomial-time approximation guarantee as POSS when the objective function is monotone, and can find an optimal solution efficiently in some cases whereas POSS cannot. Extensive experiments on unsupervised feature selection and sparse regression show the superiority of PORSS over POSS. Our analysis also theoretically discloses that recombination from diverse solutions can be more likely than mutation alone to generate various variations, thereby leading to better exploration; this may be of independent interest for understanding the influence of recombination.

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“…The Column Subset Selection Problem (CSSP) has been well-studied in the theoretical computer science literature [3,5,9,22,25,31,35]. Indeed as a dimension reduction tool for data analysis, the CSSP is completely natural.…”

Section: A Historymentioning

confidence: 99%

Perspectives on CUR decompositions

Hamm

Huang

2020

Applied and Computational Harmonic Analysis

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The CUR decomposition is a factorization of a low-rank matrix obtained by selecting certain column and row submatrices of it. We perform a thorough investigation of what happens to such decompositions in the presence of noise. Since CUR decompositions are non-uniquely formed, we investigate several variants and give perturbation estimates for each in terms of the magnitude of the noise matrix in a broad class of norms which includes all Schatten p-norms. The estimates given here are qualitative and illustrate how the choice of columns and rows affects the quality of the approximation, and additionally we obtain new state-of-the-art bounds for some variants of CUR approximations.2010 Mathematics Subject Classification. 15A23,65F30,68P99,68W20.

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Iterative column subset selection

Cited by 11 publications

References 30 publications

Unsupervised Feature Selection by Pareto Optimization

Unsupervised Feature Selection by Pareto Optimization

Subset Selection by Pareto Optimization with Recombination

Perspectives on CUR decompositions

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