tuneBSnonparRDPG {changepoints}

Change points detection for dependent dynamic random dot product graph models.

Description

Perform Change points detection for dependent dynamic random dot product graph models. The tuning parameter tau for WBS is automatically selected based on the BIC-type scores defined in Equation (2.4) in Zou et al. (2014).

Usage

tuneBSnonparRDPG(BS_object, data_mat, lowerdiag = FALSE, d)

Arguments

BS_object

A "BS" object produced by WBS.nonpar.RDPG.

data_mat

A numeric matrix of observations with horizontal axis being time, and vertical axis being vectorized adjacency matrix.

lowerdiag

A logic scalar. TRUE, if each row of data_mat is the vectorization of the strictly lower diagonal elements in an adjacency matrix. FALSE, if each row of data_mat is the vectorization of all elements in an adjacency matrix.

d

A numeric scalar of the number of leading singular values of an adjacency matrix considered in the scaled PCA algorithm.

Value

A numeric vector of estimated change points.

Author(s)

Oscar Hernan Madrid Padilla & Haotian Xu

References

Padilla, Yu and Priebe (2019) <arxiv:1911.07494>.

See Also

WBS.nonpar.RDPG.

Examples

### generate data 
p = 20 # number of nodes
n = 50 # sample size for each segment
lat_dim_num = 5 # number of latent dimensions
set.seed(1)
x_mat = matrix(runif(p*lat_dim_num), nrow = p, ncol = lat_dim_num)
x_tilde_mat = matrix(runif(p*lat_dim_num), nrow = p, ncol = lat_dim_num)
y_mat = rbind(x_tilde_mat[1:floor(p/4),], x_mat[(floor(p/4)+1):p,])
rdpg1 = simu.RDPG(x_mat, n, symm = TRUE, self = FALSE)
rdpg2 = simu.RDPG(y_mat, n, symm = TRUE, self = FALSE)
data1_mat = rdpg1$obs_mat
data2_mat = rdpg2$obs_mat
data_mat = cbind(data1_mat, data2_mat)
### detect change points
M = 20 # number of random intervals for WBS
d = 10 # parameter for scaled PCA algorithm
delta = 5
intervals = WBS.intervals(M = M, lower = 1, upper = ncol(data_mat))
WBS_result = WBS.nonpar.RDPG(data_mat, lowerdiag = TRUE, d, 
             Alpha = intervals$Alpha, Beta = intervals$Beta, delta)
cpt_hat = tuneBSnonparRDPG(WBS_result, data_mat, lowerdiag = TRUE, d)