select_r function

Cluster number selection

Estimate the cluster number in the degree-corrected tensor block model based on BIC criterion. The choice of BIC aims to balance between the goodness-of-fit for the data and the degree of freedom in the population model. This function is restricted for the Gaussian observation.

select_r(Y, r_range, asymm = FALSE)

Arguments

• Y: array/matrix, order-3 Gaussian tensor/matrix observation
• r_range: matrix, candidates for the cluster number on each row; see "details"
• asymm: logic variable, if "TRUE", clustering assignment differs in different modes; if "FALSE", all the modes share the same clustering assignment

Returns

a list containing the following:

r vector, the cluster number among the candidates with minimal BIC value

bic vector, the BIC value for each candidiate

Details

r_range should be a two-column matrix for matrix and three-column matrix for tensor observation;

all the elements in r_range should be integer larger than 1;

symmetric case only allow candidates with the same cluster number on each mode;

observations with non-identical dimension on each mode are only applicable with asymm = TRUE.

Examples

test_data = sim_dTBM(seed = 1, imat = FALSE, asymm = FALSE, p = c(50,50,50), r = c(3,3,3),
                    core_control = "control", s_min = 0.05, s_max = 1,
                    dist = "normal", sigma = 0.5,
                    theta_dist = "pareto", alpha = 4, beta = 3/4)

r_range = rbind(c(2,2,2), c(3,3,3),c(4,4,4),c(5,5,5))
selection <- select_r(test_data$Y, r_range, asymm = FALSE)