getCurves: Construct Smooth Lineage Curves
In slingshot: Tools for ordering single-cell sequencing

Description Usage Arguments Details Value References See Also Examples

This function takes a reduced data matrix n by p, a vector of cluster identities (optionally including -1's for "unclustered"), and a set of lineages consisting of paths through a forest constructed on the clusters. It constructs smooth curves for each lineage and returns the points along these curves corresponding to the orthogonal projections of each data point, along with corresponding arclength (pseudotime or lambda) values.

getCurves(sds, ...)

## S4 method for signature 'SlingshotDataSet'
getCurves(
  sds,
  shrink = TRUE,
  extend = "y",
  reweight = TRUE,
  reassign = TRUE,
  thresh = 0.001,
  maxit = 15,
  stretch = 2,
  approx_points = FALSE,
  smoother = "smooth.spline",
  shrink.method = "cosine",
  allow.breaks = TRUE,
  ...
)

## S4 method for signature 'SingleCellExperiment'
getCurves(
  sds,
  shrink = TRUE,
  extend = "y",
  reweight = TRUE,
  reassign = TRUE,
  thresh = 0.001,
  maxit = 15,
  stretch = 2,
  approx_points = FALSE,
  smoother = "smooth.spline",
  shrink.method = "cosine",
  allow.breaks = TRUE,
  ...
)

`sds`	The `SlingshotDataSet` for which to construct simultaneous principal curves. This should already have lineages identified by `getLineages`.
`...`	Additional parameters to pass to scatter plot smoothing function, `smoother`.
`shrink`	logical or numeric between 0 and 1, determines whether and how much to shrink branching lineages toward their average prior to the split.
`extend`	character, how to handle root and leaf clusters of lineages when constructing the initial, piece-wise linear curve. Accepted values are `'y'` (default), `'n'`, and `'pc1'`. See 'Details' for more.
`reweight`	logical, whether to allow cells shared between lineages to be reweighted during curve-fitting. If `TRUE`, cells shared between lineages will be iteratively reweighted based on the quantiles of their projection distances to each curve. See 'Details' for more.
`reassign`	logical, whether to reassign cells to lineages at each iteration. If `TRUE`, cells will be added to a lineage when their projection distance to the curve is less than the median distance for all cells currently assigned to the lineage. Additionally, shared cells will be removed from a lineage if their projection distance to the curve is above the 90th percentile and their weight along the curve is less than `0.1`.
`thresh`	numeric, determines the convergence criterion. Percent change in the total distance from cells to their projections along curves must be less than `thresh`. Default is `0.001`, similar to `principal_curve`.
`maxit`	numeric, maximum number of iterations, see `principal_curve`.
`stretch`	numeric factor by which curves can be extrapolated beyond endpoints. Default is `2`, see `principal_curve`.
`approx_points`	numeric, whether curves should be approximated by a fixed number of points. If `FALSE` (or 0), no approximation will be performed and curves will contain as many points as the input data. If numeric, curves will be approximated by this number of points; preferably about 100 (see `principal_curve`).
`smoother,`	choice of scatter plot smoother. Same as `principal_curve`, but `"lowess"` option is replaced with `"loess"` for additional flexibility.
`shrink.method`	character denoting how to determine the appropriate amount of shrinkage for a branching lineage. Accepted values are the same as for `kernel` in `density` (default is `"cosine"`), as well as `"tricube"` and `"density"`. See 'Details' for more.
`allow.breaks`	logical, determines whether curves that branch very close to the origin should be allowed to have different starting points.

When there is only a single lineage, the curve-fitting algorithm is nearly identical to that of principal_curve. When there are multiple lineages and shrink > 0, an additional step is added to the iterative procedure, forcing curves to be similar in the neighborhood of shared points (ie., before they branch).

The extend argument determines how to construct the piece-wise linear curve used to initiate the recursive algorithm. The initial curve is always based on the lines between cluster centers and if extend = 'n', this curve will terminate at the center of the endpoint clusters. Setting extend = 'y' will allow the first and last segments to extend beyond the cluster center to the orthogonal projection of the furthest point. Setting extend = 'pc1' is similar to 'y', but uses the first principal component of the cluster to determine the direction of the curve beyond the cluster center. These options typically have little to no impact on the final curve, but can occasionally help with stability issues.

When shink = TRUE, we compute a shrinkage curve, w_l(t), for each lineage, a non-increasing function of pseudotime that determines how much that lineage should be shrunk toward a shared average curve. We set w_l(0) = 1, so that the curves will perfectly overlap the average curve at pseudotime 0. The weighting curve decreases from 1 to 0 over the non-outlying pseudotime values of shared cells (where outliers are defined by the 1.5*IQR rule). The exact shape of the curve in this region is controlled by shrink.method, and can follow the shape of any standard kernel function's cumulative density curve (or more precisely, survival curve, since we require a decreasing function). Different choices of shrink.method seem to have little impact on the final curves, in most cases.

When reweight = TRUE, weights for shared cells are based on the quantiles of their projection distances onto each curve. The distances are ranked and converted into quantiles between 0 and 1, which are then transformed by 1 - q^2. Each cell's weight along a given lineage is the ratio of this value to the maximum value for this cell across all lineages.

An updated SlingshotDataSet object containing the oringinal input, arguments provided to getCurves as well as the following new elements:

curves A list of principal_curve objects.
slingParams Additional parameters used for fitting simultaneous principal curves.

Hastie, T., and Stuetzle, W. (1989). "Principal Curves." Journal of the American Statistical Association, 84:502–516.

slingshot

data("slingshotExample")
rd <- slingshotExample$rd
cl <- slingshotExample$cl
sds <- getLineages(rd, cl, start.clus = '1')
sds <- getCurves(sds)

plot(rd, col = cl, asp = 1)
lines(sds, type = 'c', lwd = 3)