Markov clustering (MCL) algorithm [ 15] iteratively applies "expansion" and "inflation" steps to the transition matrix that denote the Markov chain of random walk.
denotes 2-norm of matrix, that is,, where denotes the spectral radius of.
Figure 5 illustrates an example data association matrix that will be denoted as D, and Figure 6 shows some examples of D matrices, corresponding to different typical situations.
where is the DFT matrix, and is the matrix that adds the CP, with denoting the identity matrix and denoting the last columns of.
Information on genotypes is collected in an n x m matrix C, using numerical coding that denotes the number of copies of the arbitrarily defined reference allele (0, 1, 2).
where V L denotes the matrix that consists of the first L + 1 columns of K W K. Accordingly, H d ( m, n ) [ j ] can be written as H d ( m, n ) [ j ] = ∑ q = 0 Q W K D { u q } W K H D { V L c q ( m, n ) [ j ] }. (5).
Let C denote the matrix that contains those absolute correlation values between columns of S that exceed the threshold 1 - ϵ c.
d i a g{A} denotes a column vector consisting of the main diagonal elements of matrix A. d i a g{a} denotes a diagonal matrix that uses the elements of vector a as its diagonal elements.
Finally, we denote with the overall power allocation matrix, that is,.
Denote and, respectively, the expectation and the variance of the stochastic matrix, that is, (2.4).
