Table 1 Notation used in the paper

A

Matrix A

a

Vector a

\(\mathbf {A} \in \mathbb {R}_{K \times N}^{+}\)

K×N matrix whose elements are non-negative real numbers

\(\mathbf {A} \in \mathbb {R}_{K \times N}\)

K×N matrix whose elements are real numbers

1 _{K× N}

A K×N matrix whose elements are all one.

a_(k,n) or [A]_(k,n)

An element of the matrix A in k-th row and n-th column

a ^{( t)}

The updated value of a after t iterations

A⊗B

Hadamard (elementwise) multiplication of A and B

A/B

Elementwise division of A and B

A ^T

Transpose of A

A _{↑ d}

Upward shift of matrix A by d rows

A _{← d}

Left shift of matrix A by d columns

A _{→ d}

Right shift of matrix A by d columns

∇_AC

The gradient of C with respect to A

\(\nabla ^{+}_{\mathbf {A}}C\)

Positive parts of the gradient of C with respect to A

\(\nabla ^{-}_{\mathbf {A}}C\)

Negative parts of the gradient of C with respect to A