ddpca (version 1.1)

ProjDD: Projection onto the Diagonally Dominant Cone

Description

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

Usage

ProjDD(C)

Arguments

C

A \(n \times n\) matrix

Value

A \(n\times n\) diagonally dominant matrix

Details

This function projects the input matrix \(C\) of size \(n\times n\) onto the cones of diagonally domimant matrices defined as $$ \{A = (a_{ij})_{1\le i\le n, 1\le j\le n} : a_{jj} \ge \sum_{k\not=j} |a_{jk}| \quad \textrm{for all} \quad 1\le j\le n \}$$ The algorithm is described in Mendoza, M., Raydan, M. and Tarazaga, P., 1998. Computing the nearest diagonally dominant matrix.

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.

See Also

ProjSDD

Examples

# NOT RUN {
ProjDD(matrix(runif(100),nrow=10))
# }