# ProjDD: Projection onto the Diagonally Dominant Cone In ddpca: Diagonally Dominant Principal Component Analysis

## Description

Given a matrix C, this function outputs the projection of C onto the cones of diagonally domimant matrices.

## Usage

 1 ProjDD(C) 

## Arguments

 C A n \times n matrix

## Details

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

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

The algorithm is described in Mendoza, M., Raydan, M. and Tarazaga, P., 1998. Computing the nearest diagonally dominant matrix.

## Value

A n\times n diagonally dominant matrix

## Author(s)

Fan Yang <fyang1@uchicago.edu>

## References

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.

ProjSDD

## Examples

 1 ProjDD(matrix(runif(100),nrow=10)) 

### Example output

            [,1]       [,2]        [,3]      [,4]      [,5]      [,6]
[1,] 1.18781379 0.01158890 0.358406851 0.0000000 0.0000000 0.0000000
[2,] 0.08910637 1.08352450 0.000000000 0.0000000 0.0000000 0.3108263
[3,] 0.00000000 0.00000000 0.977764374 0.0000000 0.0000000 0.0000000
[4,] 0.15737312 0.00000000 0.000000000 0.7574381 0.2042491 0.0000000
[5,] 0.28370274 0.00000000 0.149296133 0.0000000 1.2735160 0.0000000
[6,] 0.19940393 0.00000000 0.048533858 0.0000000 0.0000000 0.8350456
[7,] 0.16010142 0.00000000 0.000000000 0.3890597 0.0000000 0.0000000
[8,] 0.32080217 0.01409226 0.000000000 0.0000000 0.2768446 0.2296203
[9,] 0.00000000 0.00000000 0.261620528 0.0000000 0.3752784 0.0000000
[10,] 0.06524040 0.42279541 0.005576454 0.0000000 0.3975106 0.1794841
[,7]      [,8]      [,9]      [,10]
[1,] 0.27088398 0.5469341 0.0000000 0.00000000
[2,] 0.08119593 0.2258320 0.0000000 0.37656387
[3,] 0.00000000 0.1620120 0.4919782 0.32377411
[4,] 0.09884490 0.2428527 0.0000000 0.05411831
[5,] 0.21074208 0.0000000 0.6297750 0.00000000
[6,] 0.00000000 0.3951430 0.1919649 0.00000000
[7,] 1.18732863 0.2047038 0.3456207 0.08784303
[8,] 0.00000000 1.0813378 0.0000000 0.23997839
[9,] 0.00000000 0.3081468 1.0266079 0.08156215
[10,] 0.00000000 0.0000000 0.2656341 1.33624111


ddpca documentation built on Sept. 15, 2019, 1:03 a.m.