scholarly journals SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression

2015 ◽  
Vol 246 (1) ◽  
pp. 44-50
Author(s):  
Salvador Flores
Keyword(s):  
Linear Regression ◽  
Subset Selection ◽  
Selection Problem ◽  
Optimal Subset ◽  
Robust Linear Regression

Hypervolume Subset Selection with Small Subsets

2019 ◽  
Vol 27 (4) ◽  
pp. 611-637
Author(s):  
Benoît Groz ◽  
Silviu Maniu
Keyword(s):  
Evolutionary Algorithms ◽  
Subset Selection ◽  
Higher Dimensions ◽  
Efficient Algorithms ◽  
Selection Problem ◽  
Multiobjective Evolutionary Algorithms ◽  
Optimal Subset ◽  
Arbitrary Dimensions ◽  
Hypervolume Indicator

The hypervolume subset selection problem (HSSP) aims at approximating a set of [Formula: see text] multidimensional points in [Formula: see text] with an optimal subset of a given size. The size [Formula: see text] of the subset is a parameter of the problem, and an approximation is considered best when it maximizes the hypervolume indicator. This problem has proved popular in recent years as a procedure for multiobjective evolutionary algorithms. Efficient algorithms are known for planar points ([Formula: see text]), but there are hardly any results on HSSP in larger dimensions ([Formula: see text]). So far, most algorithms in higher dimensions essentially enumerate all possible subsets to determine the optimal one, and most of the effort has been directed toward improving the efficiency of hypervolume computation. We propose efficient algorithms for the selection problem in dimension 3 when either [Formula: see text] or [Formula: see text] is small, and extend our techniques to arbitrary dimensions for [Formula: see text].

scholarly journals Motor unit innervation zone localization based on robust linear regression analysis

2019 ◽  
Vol 106 ◽  
pp. 65-70 ◽  
Author(s):  
Jie Liu ◽  
Sheng Li ◽  
Faezeh Jahanmiri-Nezhad ◽  
William Zev Rymer ◽  
Ping Zhou
Keyword(s):  
Regression Analysis ◽  
Linear Regression ◽  
Motor Unit ◽  
Linear Regression Analysis ◽  
Innervation Zone ◽  
Robust Linear Regression

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.

On Selecting a Subset Containing the Alternative with the Largest Priority

1994 ◽  
Vol 44 (1-2) ◽  
pp. 41-48
Author(s):  
Tong-An Hsu
Keyword(s):  
Decision Problem ◽  
Subset Selection ◽  
Selection Procedure ◽  
Selection Problem ◽  
Ratio Scale

Let A1, A2,…, A k be k alternatives for a decision problem. Saaty uses ratio scale (π1, π2,…, π k) for the priorities of the alternatives. In a subset selection problem, we derive some selection procedure to select a subset from the k alternatives which includes the largest priority.

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