2020
DOI: 10.1007/s00180-020-00963-7
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Ultra-high dimensional variable screening via Gram–Schmidt orthogonalization

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Cited by 3 publications
(2 citation statements)
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“…Gram-Schmidt Orthogonalization (GSO) is adopted in this paper to decompose and identify the information contained in the predictor set, and further to measure multicollinearity among predictors (Lyu et al, 2017;Wang et al, 2020). The Gram-Schmidt theorem in Euclidean space indicates that for an index subset of predictors G = {g 1 , ⋯, g q } ⊆ X and the corresponding matrix X G = (X g1 , ⋯, X gq ), if X G is linearly independent, one can always construct an orthogonal basis Z G = (Z g1 , ⋯, Z gq ) via GSO, where Z G is the linear combination of X G , and it spans the same space as X G .…”
Section: The Redundant Subset and Its Measurementioning
confidence: 99%
“…Gram-Schmidt Orthogonalization (GSO) is adopted in this paper to decompose and identify the information contained in the predictor set, and further to measure multicollinearity among predictors (Lyu et al, 2017;Wang et al, 2020). The Gram-Schmidt theorem in Euclidean space indicates that for an index subset of predictors G = {g 1 , ⋯, g q } ⊆ X and the corresponding matrix X G = (X g1 , ⋯, X gq ), if X G is linearly independent, one can always construct an orthogonal basis Z G = (Z g1 , ⋯, Z gq ) via GSO, where Z G is the linear combination of X G , and it spans the same space as X G .…”
Section: The Redundant Subset and Its Measurementioning
confidence: 99%
“…The standard orthogonal basis is obtained by a basis in the inner product space formed by the input connection weight matrix W in based on the Schmidt orthogonalization method . An example of orthogonalization of two linearly independent vectors α 1 and α 2 is obtained as follows: …”
Section: Methodsmentioning
confidence: 99%