Table 1 Notations

\(A \in {\mathcal{R}}^{m \times n}\)

Capital case letter generally denotes a matrix of size m × n

\(a \in {\mathcal{R}}^{m}\)

Lower case letter denotes a column vector of length m

A _ij or a _i

A scalar/element from the matrix at location (i,j) or a vector element at i

||A|| _F

\(\sqrt {\mathop \sum \nolimits_{i = 1}^{m} \mathop \sum \nolimits_{j = 1}^{n} A_{ij}^{2} }\)—square root of the sum of the squares of all the elements of the matrix

||A||₁

\(\sum\nolimits_{i = 1}^{m} {\sum\nolimits_{j = 1}^{n} {\left| {A_{ij} } \right|} }\)—sum of absolute values of all the elements. Here absolute value means the non-negative value without its sign

||a||₂

\(\sqrt {\sum\nolimits_{i = 1}^{m} {a_{i}^{2} } }\)—square root of the sum of the squares of all the elements of the vector

μ

Mean of a vector

KL(P||Q)

Defines the similarity between two matrices P and \(Q\) as \(\sum\nolimits_{i = 1}^{m} {\sum\nolimits_{j = 1}^{n} {\left( {P_{ij} \log \frac{{P_{ij} }}{{Q_{ij} }} } \right)} }\)