scholarly journals Column Subset Selection Problem is UG-hard

2014 ◽  
Vol 80 (4) ◽  
pp. 849-859 ◽  
Author(s):  
A. Çivril
Keyword(s):  
Subset Selection ◽  
Selection Problem ◽  
Column Subset Selection

scholarly journals Optimality of Spectrum Pursuit for Column Subset Selection Problem: Theoretical Guarantees and Applications in Deep Learning

2020 ◽  
Author(s):  
Mohsen Joneidi ◽  
Saeed Vahidian ◽  
Ashkan Esmaeili ◽  
Siavash Khodadadeh
Keyword(s):  
Deep Learning ◽  
Upper Bound ◽  
Linear Complexity ◽  
Subset Selection ◽  
Selection Problem ◽  
Theoretical Methods ◽  
Novel Technique ◽  
Original Dataset ◽  
Column Subset Selection ◽  
Minimum Number

We propose a novel technique for finding representatives from a large, unsupervised dataset. The approach is based on the concept of self-rank, defined as the minimum number of samples needed to reconstruct all samples with an accuracy proportional to the rank-$K$ approximation. Our proposed algorithm enjoys linear complexity w.r.t. the size of original dataset and simultaneously it provides an adaptive upper bound for approximation ratio. These favorable characteristics result in filling a historical gap between practical and theoretical methods in finding representatives.<br>

scholarly journals Optimality of Spectrum Pursuit for Column Subset Selection Problem: Theoretical Guarantees and Applications in Deep Learning

2020 ◽  
Author(s):  
Mohsen Joneidi ◽  
Saeed Vahidian ◽  
Ashkan Esmaeili ◽  
Siavash Khodadadeh
Keyword(s):  
Deep Learning ◽  
Upper Bound ◽  
Linear Complexity ◽  
Subset Selection ◽  
Selection Problem ◽  
Theoretical Methods ◽  
Novel Technique ◽  
Original Dataset ◽  
Column Subset Selection ◽  
Minimum Number

We propose a novel technique for finding representatives from a large, unsupervised dataset. The approach is based on the concept of self-rank, defined as the minimum number of samples needed to reconstruct all samples with an accuracy proportional to the rank-$K$ approximation. Our proposed algorithm enjoys linear complexity w.r.t. the size of original dataset and simultaneously it provides an adaptive upper bound for approximation ratio. These favorable characteristics result in filling a historical gap between practical and theoretical methods in finding representatives.<br>

A Distributed Integrated Feature Selection Scheme for Column Subset Selection

2021 ◽  
pp. 1-1
Author(s):  
Zheng Xiao ◽  
Pengcheng Wei ◽  
Anthony Chronopoulos ◽  
Anne C. Elster
Keyword(s):  
Feature Selection ◽  
Subset Selection ◽  
Selection Scheme ◽  
Column Subset Selection

scholarly journals Unsupervised Band Selection Method Based on Importance-Assisted Column Subset Selection

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 517-527 ◽  
Author(s):  
Xiaoyan Luo ◽  
Zhiqi Shen ◽  
Rui Xue ◽  
Han Wan
Keyword(s):  
Subset Selection ◽  
Selection Method ◽  
Band Selection ◽  
Column Subset Selection

scholarly journals Finding Points in General Position

2017 ◽  
Vol 27 (04) ◽  
pp. 277-296 ◽  
Author(s):  
Vincent Froese ◽  
Iyad Kanj ◽  
André Nichterlein ◽  
Rolf Niedermeier
Keyword(s):  
Lower Bound ◽  
General Position ◽  
Subset Selection ◽  
Selection Problem ◽  
Fixed Parameter Tractability ◽  
Maximum Cardinality ◽  
Exponential Time ◽  
Running Time ◽  
Fixed Parameter ◽  
Set Of Points

We study the General Position Subset Selection problem: Given a set of points in the plane, find a maximum-cardinality subset of points in general position. We prove that General Position Subset Selection is NP-hard, APX-hard, and present several fixed-parameter tractability results for the problem as well as a subexponential running time lower bound based on the Exponential Time Hypothesis.

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