hydraPlus {hydra}

hydra with additional stress minimization

Description

Runs the hydra method and then performs a further optimization step by minimizing the stress of the embedding and optimizing hyperbolic curvature

Usage

hydraPlus(D, dim = 2, curvature = 1, alpha = 1.1, equi.adj = 0.5,
  control = list(), curvature.bias = 1, curvature.freeze = TRUE,
  curvature.max = NULL, maxit = 1000, ...)

Arguments

D

a square symmetric matrix of distances (or dissimiliarities) to be embdedded, can also be a dist object

dim

embedding dimension

curvature

embedding curvature; if this argument is NULL, hydra tries to find the optimal curvature

alpha

real number greater one; adjusts the hyperbolic curvature. Values larger than one yield a more distorted embedding where points are pushed to the outer boundary (i.e. the ideal points) of hyperblic space. The interaction between curvature and alpha is non-linear.

equi.adj

equi-angular adjustment; must be a real number between zero and one; only used if dim is 2. Value 0 means no ajustment, 1 adjusts embedded data points such that their angular coordinates in the Poincare disc are uniformly distributed. Other values interpolate between the two extremes. Setting the parameter to non-zero values can make the embedding result look more harmoniuous in plots.

control

a list which may contain the following boolean flags:

• polar - return polar coordinates in dimension 2 (default: TRUE if dim is 2. This flag is ignored in higher dimension)

• isotropic.adj - perform isotropic adjustment, ignoring Eigenvalues (default: TRUE if dim is 2, FALSE else)

• return.lorentz - return raw Lorentz coordinates (before projection to hyperbolic space) (default: FALSE)

• return.stress - return embedding stress (default: TRUE)

• return.dist - return hyperbolic distance matrix of embedded points (default: FALSE)

• use.eigs - use eigs function from RSpectra and norm function from Matrix to speed up computation (default: FALSE)

curvature.bias

Modify curvature before stress minimization by multiplying with curvature.bias

curvature.freeze

Freeze the curvature returned by hydra. If TRUE then no optimization of curvature is attempted in the second stage of the algorithm. If FALSE then curvature is optimized in the second stage

curvature.max

Upper bound for the curvature. If NULL, a defulat bound is used

maxit

Maximal number of iterations. This parameter is passed to the optimization routine optim

...

Additional parameters are passed to optim, which performs the underlying stress minimization

Details

See https://arxiv.org/abs/1903.08977 for more details.

Value

A ‘hydra’ object, which is a list with all or some of the following components:

r

a vector containing the radial coordinates of the embedded points

directional

a matrix with dim columns containing as rows the directional coordinates of the embedded points

theta

a vector containing the angular coordinates of the embedded points (only returned if dim is 2 and polar flag is TRUE)

curvature

the curvature used for the returned embedding

dim

the dimension used for the returned embedding

stress

the stress (i.e. the mean-square difference) between distances supplied in D and the hyperbolic distance matrix of the returned embedding

dist

the hyperbolic distance matrix of the returned embedding (only returned if flag return.dist is true. Computation may be time- and memory-intensive.)

x0

a vector containing the 'time-like' coordinate of the raw Lorentz embedding (only returned if flag return.lorentz is true)

X

a matrix with dim columns containing as rows the 'space-like' coordinate of the raw Lorentz embedding (only returned if flag return.lorentz is true)

Author(s)

Martin Keller-Ressel <[e-mail]>

Examples

data(karate)
embedding <- hydraPlus(karate$distance)
plot(embedding,labels=karate$label,node.col=karate$group,graph.adj=karate$adjacency)