FindOpt_SimplifiedCase: Function that calculates the optimal low-rank signal matrix...

In justicesuker/DMMD_Package: Double Matched Matrix Decomposition

Function that calculates the optimal low-rank signal matrix given partial column and row space basis.

Description

Function that calculates the optimal low-rank signal matrix given partial column and row space basis.

Usage

FindOpt_SimplifiedCase(X, M, N, r)

Arguments

X	The noisy matrix (n by p)
M	The column space that the output signal matrix contains (n by r_c )
N	The row space that the output signal matrix contains (p by r_r )
r	The rank of output signal matrix ( r = max(r_c, r_r) )

Details

This function only works when either the rank of M (column space basis) or N (row space basis) equal to the specified rank r (

r = max(r_c, r_r)

). It's a prerequisite of 'FindOpt_DM_Iterative' function. The resulting matrix is the solution to the following problem:

min_{Y}{||X - Y||^2_F}

subject to

M is a subset of column space of Y, N is a subset of row space of Y

Value

A list with the following elements:

result	A matrix that is the solution to the optimization problem
R	The remaining r - r_c number of column bases
S	The remaining r - r_r column bases

justicesuker/DMMD_Package documentation built on Aug. 6, 2022, 12:34 p.m.