Fit Smooth-Spline Curves to the Mean/Median 3D Trajectory — fit.trajectory.smooth.splines • gflow

Given a 3D embedding of graph vertices and a list of trajectories (each a vector of vertex indices), this function:

resamples all trajectories to a common length (to make them comparable),
computes a pointwise mean or median trajectory in 3D,
fits a smooth spline to each coordinate as a function of trajectory index.

The spline fit for coordinate i uses: $$fit_i = stats::smooth.spline(x = seq_along(y_i), y = y_i, df = df)$$ where $y_i$ is the i-th coordinate of the mean/median trajectory.

Usage

fit.trajectory.smooth.splines(
  embed.3d,
  trajectories,
  df = NULL,
  center = c("mean", "median"),
  target.length = NULL,
  grid.length = NULL
)

Arguments

embed.3d: Numeric matrix/data.frame with exactly 3 columns; row r gives the 3D coordinates for vertex r (1-based indexing).
trajectories: List of integer vectors; each vector is a trajectory of vertex indices (1-based). Trajectories may have different lengths.
df: Degrees of freedom passed to stats::smooth.spline. If NULL, GCV-based selection is used by smooth.spline.
center: One of "mean" or "median"; how to compute the representative (pointwise) trajectory after resampling.
target.length: Integer common length used after resampling. If NULL, uses round(stats::median(lengths(trajectories))).
grid.length: Integer number of points on which to evaluate the fitted splines for the returned smoothed curve. If NULL, uses target.length.

Value

A list with class "gfc_mean_trajectory_spline" containing:

center: Centering method used: "mean" or "median".
df: Degrees of freedom used (input df; may be NULL).
target.length: Common resampling length used.
t: Integer vector 1:target.length.
t.grid: Numeric vector for spline evaluation (length grid.length).
traj.center: Matrix (target.length x 3): pointwise mean/median trajectory.
fits: List of three smooth.spline objects (x/y/z).
traj.smooth: Matrix (grid.length x 3): spline-smoothed trajectory.
resampled.trajs: List of matrices; each is (target.length x 3) resampled coordinates.

Examples

if (FALSE) { # \dontrun{
res <- fit.trajectory.smooth.splines(embed.3d, trajectories, df = NULL, center = "median")
plot(res$traj.smooth[,1], res$traj.smooth[,2], type = "l")
} # }