ProjSDD: Projection onto the Symmetric Diagonally Dominant Cone
In ddpca: Diagonally Dominant Principal Component Analysis

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/ProjSDD.R

Given a matrix C, this function outputs the projection of C onto the cones of symmetric diagonally domimant matrices using Dykstra's projection algorithm.

1	ProjSDD(A, max_iter_SDD = 20, eps = NA)

`A`	Input matrix of size n\times n
`max_iter_SDD`	Maximal number of iterations of the Dykstra's projection algorithm
`eps`	The iterations will stop either when the Frobenious norm of difference matrix between two updates is less than `eps` or after `max_iter_SDD` steps. If set to `NA`, then no check will be done during iterations and the iteration will stop after `max_iter_SDD` steps. Default is `NA`.

This function projects the input matrix C of size n\times n onto the cones of symmetric diagonally domimant matrices defined as

\{A = (a_{ij})_{1≤ i≤ n, 1≤ j≤ n} : a_{ij} = a_{ji}, a_{jj} ≥ ∑_{k\not=j} |a_{jk}| \quad \textrm{for all} \quad 1≤ j≤ n, 1≤ i≤ n \}

It makes use of Dykstra's algorithm, which is a variation of iterative projection algorithm. The two key steps are projection onto the diagonally domimant cone by calling function ProjDD and projection onto the symmetric matrix cone by simple symmetrization.

More details can be found in Mendoza, M., Raydan, M. and Tarazaga, P., 1998. Computing the nearest diagonally dominant matrix.

A n\times n symmetric diagonally dominant matrix

Fan Yang <fyang1@uchicago.edu>

Mendoza, M., Raydan, M. and Tarazaga, P., 1998. Computing the nearest diagonally dominant matrix. Numerical linear algebra with applications, 5(6), pp.461-474.

Ke, Z., Xue, L. and Yang, F., 2019. Diagonally Dominant Principal Component Analysis. Journal of Computational and Graphic Statistics, under review.

ProjDD