R/pre_define_functions.r
RSAVS_S_to_Groups.RdThis function converts the augmented pair-wise difference vector(the s vector in the algorithm) to the subgrouping result.
RSAVS_S_to_Groups(s_vec, n)the s vector(pair-wise difference vector), length n * (n - 1) / 2 and
\(s_{ij} = \mu_i - \mu_j\).
number of observations.
a list containing the grouping result.
Detailed definition of the s vector(length n * (n - 1) / 2) can be found in the paper.
It's possible that there's logical contradiction in the s vector,
e.g. s_{12} = s_{13} = 0, but s_{23} != 0, especially when the algorithm is
configured with a loose tolerance. In this function, i and j would be put in the
same subgroup as long as there is a path that connects them. In previous example, 1st, 2nd and
3rd observations will be classified as in the same subgroup even though s_{23} != 0.
This strategy would presumably provide a more concentrate results, hence less number of subgroups. But of course it tends to merge subgroups into big ones and leaving some alone observations.
For large scale data, especially when the number observation is big. It will be difficult to save
all s_vecs during the algorithm considering the algorithm have to search over the
lam1_length * lam2_length grid. During the algorithm, the s_vec is utilized to
improve the subgrouping results then discarded.
n <- 10 # number of observations
group_center <- c(-1, 0, 1) # three group centers
# subgroup effect vector
alpha_true <- sample(group_center, size = n, replace = TRUE)
d_mat <- RSAVS:::RSAVS_Generate_D_Matrix(n) # pair-wise difference matrix
s_vec <- d_mat %*% alpha_true
RSAVS:::RSAVS_S_to_Groups(s_vec, n)
#> [[1]]
#> [1] 1 3 5 7
#>
#> [[2]]
#> [1] 2 6 8 9 10
#>
#> [[3]]
#> [1] 4
#>
# if there's contradiction in s_vec
s_vec[1] <- 0 # s_{12} = 0
s_vec[2] <- 0 # s_{13} = 0
s_vec[n] <- 1 # s_{23} != 0
# 1, 2, 3 will still be in the same subgroup
RSAVS:::RSAVS_S_to_Groups(s_vec, n)
#> [[1]]
#> [1] 1 2 3 5 6 7 8 9 10
#>
#> [[2]]
#> [1] 4
#>