Find a hyperbolic base point via multi-start optimization.

Hyperbolic case of optimize_base_point: numerically minimizes the total hyperbolic distance (dist_hyperbolic) from a candidate point p to every row of X. The search is unconstrained, over the tangent space at the Lorentzian centroid (auto_base_point_hyperbolic), with restarts drawn from a Gaussian scaled to the spread of the data. See choose_base_point.

Usage

optimize_base_point_hyperbolic(X, n_start = 10, maxit = 200, seed = 42)

Arguments

X

A matrix or data frame of points on the hyperboloid; rows are samples, with d + 1 columns.

n_start

Number of random restarts used to avoid local minima of the (non-convex) objective. Defaults to 10.

maxit

Maximum number of optim iterations per restart. Defaults to 200.

seed

Integer random seed used to generate the restart points, for reproducibility. Defaults to 42.

Value

A list with three elements: p (the best point found across all restarts, on the hyperboloid), value (its total hyperbolic distance to the rows of X), and convergence (the optim convergence code of the best restart; 0 indicates successful convergence).

Examples

X <- exp_map_hyperbolic(matrix(rnorm(20), nrow = 10, ncol = 2))
optimize_base_point_hyperbolic(X, n_start = 5)
#> $p
#> [1] 1.1809631 0.5031822 0.3761403
#> 
#> $value
#> [1] 10.85483
#> 
#> $convergence
#> [1] 0
#>