Description Usage Arguments Details Value Author(s) References See Also Examples
hierarchy
computes the hierarchy of a hierarchical block matrix computed with hbm
.
1 | hierarchy(hm)
|
hm |
a hierarchical block matrix computed with |
In a hierarchical matrix, computed with hbm
, the behavior around the diagonal reflects the hierarchy of the association matrix. Specifically, for a hierarchical fractal-like structure we expect a non-decreasing series in the upper triangle of the matrix and a non-increasing series in the lower triangle. hierarchy
counts the number of deviations from this behavior for each node: number of negative successive differences up to the diagonal and number of positive successive changes after the diagonal, and returns the negation of the mean number of changes across nodes.
hierarchy
returns a numeric value giving the hierarchy of the matrix.
Yoli Shavit
hbm
's website: http://www.cl.cam.ac.uk/~ys388/hbm/
generate.random.conf
to see how to generate interesting chains
hbm
learn how to build hierarchical block matrices
hbm
's tutorials at http://www.cl.cam.ac.uk/~ys388/hbm/
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | set.seed(2)
n = 100 # chain size
#generate configurations
conf = generate.random.conf(n, sd = 0.5, scale = FALSE)
#perturb the chain
conf.perturb.all = generate.random.conf(n, perturb = 1:n, sd = 0.5, scale = FALSE)
# and again with less perturbration
conf.perturb = generate.random.conf(n, perturb = 10:50, sd = 0.5, scale = FALSE)
# compute the HBMs
hm.control = hbm(exp(-1*as.matrix(dist(conf))), 2)$hm
hm.perturb.all = hbm(exp(-1*as.matrix(dist(conf.perturb.all))), 2)$hm
hm.perturb = hbm(exp(-1*as.matrix(dist(conf.perturb))), 2)$hm
h.control = hierarchy(hm.control)
h.perturb = hierarchy(hm.perturb)
h.perturb.all = hierarchy(hm.perturb.all)
h = c(h.control, h.perturb, h.perturb.all)
# plot
plot(1:3, h, pch = 19, cex = 2, axes = FALSE, ylab = "Chain Hierarchy", xlab = "Condition")
axis(1, at = 1:3, labels = c("Control", "Perturbed-Partial", "Perturbed-All"))
axis(2)
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