Generalizing the Singular Value Decomposition

By Charles F. Van Loan. 1976

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Citations in the corpus

On Learning the Geodesic Path for Incremental Learning (2021, methodology): “In the supplementary material of our paper, we provide more details about the geodesic flow on Grassmannian and how R, Γ(ν) and Σ(ν) can be obtained from P t−1 and P t. Note that both P⊤t−1P t and R ⊤P t share the same right singular vectors V , thus generalized Singular Value Decomposition (SVD) [3”
Graph Embedding Techniques, Applications, and Performance: A Survey (2017, methodology): “This enables HOPE to use generalized Singular Value De-composition (SVD) [30] to obtain the embedding efﬁciently.”
Using discriminant analysis for multi-class classification: an experimental investigation (2006, unknown): “( 2001 ) presented an algorithm for dimensional reduction for text representation based on cluster structure preserving projection using generalized singular value decomposition ( GSVD ) .”
Secure Transmission With Multiple Antennas—Part II: The MIMOME Wiretap Channel (2010, methodology): “Channel Decomposition For some of our analysis, it will be convenient to exploit the generalized singular value decomposition (GSVD) [25], [26] of the channel (1).”
THE REFLEXIVE RE-NONNEGATIVE DEFINITE SOLUTION TO A QUATERNION MATRIX EQUATION ∗ (2008, unknown): “1 can be regarded as an extension of the generalized singular value decomposition (GSVD) on a complex matrix pair (see [31]-[33]).”
A two-stage linear discriminant analysis via QR-decomposition (2005, unknown): “The common point of these LDA extensions is the use of Singular Value Decomposition (SVD) [10] or Generalized Singular Value Decomposition (GSVD) [31], which not only degrades the training efficiency but also makes them hard to scale to large data sets.”
Generalizing discriminant analysis using the generalized singular value decomposition (2004, methodology): “The following theorem introduces the GSVD as it was originally defined by Van Loan [ 20 ].”