On the largest principal angle between random subspaces

By Pierre-Antoine Absil, Alan Edelman, Plamen Koev. 2006

88 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/69a17e27c599c7fe4ef3070e0313b20664d7604b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Environmental Engineering

Tiefeng Jiang

In Geometry and Topology

Citations in the corpus

Principal Component Analysis: A Method for Determining the Essential Dynamics of Proteins (2014, background): “Common metrics that quantify SS similarity include cumulative overlap (CO), root mean square inner product (RMSIP), and principal angles (PA) [12, 41–45].”
On differentially private low rank approximation (2013, background): “The distribution of the canonical angle between two uniformly random subspaces is given by [1] where ([14]) ) .”
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization (2007, background): “ciated with each subspace. This distance measures the operator norm of the dierence between the corresponding projections, and is equal to the sine of the largest principal angle between T 1 and T 2 [1]. 16 The set of all d-dimensional subspaces of RDis commonly known as the Grassmannian manifold G(”
Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength (2013, methodology): “Observe that under Q uΩ Y , the squares of the sines of the principle angles between span( I n,t ) and Ω have the same distribution as the eigenvalues of a complex multivariate Beta-distributed matrix B ∼ Beta r ( n t, t ) [36, Sec.”
Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles (2009, methodology): “…two rows of matrices in Table 1 and for β = 1, 2, 4, the circular law, the semi-circular law, the Marchenko-Pastur law of eigenvalues, the strong law of largest eigenvalues, the TracyWidom distribution for the largest eigenvalues had been derived, respectively, by many authors since Wigner[70].”