Estimate C matrix from an Advantage/Disadvantage matrix

Use this function to estimate a possible C matrix from a skew-symmetric A matrix. Recall that \(A = C \Omega C'\). Combined with est_A_from_data(), this might be useful for warm starting mELO models.

est_C_given_A(A_mat, k = 1)

Arguments

A_mat	An advantage/disadvantage matrix.
k	The number of columns of the C matrix. More complex non-transitive interactions require higher values of k.

Value

A list with three components:

C_mat

The estimated C matrix

error

The squared reconstruction error

est_req_k

The estimated required value for k to minimise the reconstruction error.

Examples

# Generate C mat
set.seed(112123)
m <- 4
k <- 1
C_mat <- matrix(
    runif(m*2*k, 0, 10),
  ncol = 2*k
)


Omega_mat <- construct_omega(k)
A_mat <- C_mat %*% Omega_mat %*% t(C_mat)
A_mat
#>           [,1]      [,2]       [,3]      [,4]
#> [1,]   0.00000 16.926723  14.033027 27.323039
#> [2,] -16.92672  0.000000  -8.399661  1.470011
#> [3,] -14.03303  8.399661   0.000000 14.777401
#> [4,] -27.32304 -1.470011 -14.777401  0.000000

C_mat_list <- find_C_given_A(A_mat)
#> Error in find_C_given_A(A_mat): could not find function "find_C_given_A"
C_mat_list
#> Error in eval(expr, envir, enclos): object 'C_mat_list' not found