WBS.nonpar.RDPG {changepoints}

Wild binary segmentation for dependent dynamic random dot product graph models.

Description

Perform wild binary segmentation for dependent dynamic random dot product graph models.

Usage

WBS.nonpar.RDPG(data_mat, lowerdiag = FALSE, d, Alpha, Beta, delta)

Arguments

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.

Alpha

A integer vector of starting indices of random intervals.

Beta

A integer vector of ending indices of random intervals.

delta

A positive integer scalar of minimum spacing.

Value

An object of class "BS", which is a list with the following structure:

S

A vector of estimated change point locations (sorted in strictly increasing order).

Dval

A vector of values of CUSUM statistic.

Level

A vector representing the levels at which each change point is detected.

Parent

A matrix with the starting indices on the first row and the ending indices on the second row.

Author(s)

Oscar Hernan Madrid Padilla, Haotian Xu

References

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

See Also

thresholdBS for obtaining change points estimation, tuneBSnonparRDPG for a tuning version.

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 = 30 # 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)