depthc.Tukey: Calculate Tukey curve depth for curves
In curveDepth: Tukey Curve Depth and Distance in the Space of Curves

Description Usage Arguments Details Value References Examples

Calculates Tukey curve depth of each curve in objects w.r.t. the sample of curves in data. First, m points are sampled from a uniform distribution on a piecewise linear approximation of each of the curves in data and m / fracEst * (fracInt + fracEst) points on each of the curves in objects. Second, these samples are used to calculate the Tukey curve depth.

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depthc.Tukey(objects, data, nDirs = 100L, subs = TRUE, m = 500L,
  fracInt = 0.5, fracEst = 0.5, exactEst = TRUE, minMassObj = 0,
  minMassDat = 0)

`objects`	A list where each element is a multivariate curve being a list containing a matrix `coords` (values, d columns).
`data`	A list where each element is a multivariate curve being a list containing a matrix `coords` (values, d columns). The depths are computed w.r.t. this data set.
`nDirs`	Number of directions used to inspect the space, drawn from the uniform distribution on the sphere.
`subs`	Whether to split each object into two disjunctive subsets (one for integrating and one for estimation) when computing the depth.
`m`	Number of points used for estimation.
`fracInt`	Portion of an object used for integrating.
`fracEst`	Portion of an object used for estimation, maximum: `1 - fracInt`.
`exactEst`	Is calculation of depth for each reference point of the curve exact (`TRUE`, by default) or approximate (`FALSE`).
`minMassObj`	Minimal portion of the `objects` distribution in the halfspace to be considered when calculating depth.
`minMassDat`	minimal portion of the `data` distribution in the halfspace to be considered when calculating depth.

Calculation of partial depth of each single point can be either exact or approximate. If exact, an extension of the method of Dyckerhoff and Mozharovskyi (2016) is used; if approximate, approximation is performed by projections on directions - points uniformly distributed on the unit hypersphere.

A vector of doubles having the same length as objects, whose each entry is the depth of each element of objects w.r.t. data.

Lafaye De Micheaux, P., Mozharovskyi, P. and Vimond, M. (2018). Depth for curve data and applications.

Dyckerhoff, R. and Mozharovskyi P. (2016). Exact computation of the halfspace depth. Computational Statistics and Data Analysis, 98, 19-30.

library(curveDepth)
# Load digits and transform them to curves
data("mnistShort017")
n <- 10 # cardinality of each class
m <- 50 # number of points to sample
cst <- 1/10 # a threshold constant
alp <- 1/8 # a threshold constant
curves0 <- images2curves(mnistShort017$`0`[, , 1:n])
curves1 <- images2curves(mnistShort017$`1`[, , 1:n])
# Calculate depths
depthSpace = matrix(NA, nrow = n * 2, ncol = 2)
set.seed(1)
depthSpace[, 1] = depthc.Tukey(
  c(curves0, curves1), curves0, m = m,
  exactEst = TRUE, minMassObj = cst/m^alp)
depthSpace[, 2] = depthc.Tukey(
  c(curves0, curves1), curves1, m = m,
  exactEst = TRUE, minMassObj = cst/m^alp)
# Draw the DD-plot
plot(NULL, xlim = c(0, 1), ylim = c(0, 1),
     xlab = paste("Depth w.r.t. '0'"),
     ylab = paste("Depth w.r.t. '1'"),
     main = paste("DD-plot for '0' vs '1'"))
grid()
# Draw the separating rule
dat1 <- data.frame(cbind(
  depthSpace, c(rep(0, n), rep(1, n))))
ddalpha1 <- ddalpha.train(X3 ~ X1 + X2, data = dat1,
                          depth = "ddplot",
                          separator = "alpha")
ddnormal <- ddalpha1$classifiers[[1]]$hyperplane[2:3]
pts <- matrix(c(0, 0, 1, ddnormal[1] / -ddnormal[2]),
              nrow = 2, byrow = TRUE)
lines(pts, lwd = 2)
# Draw the points
points(depthSpace[1:n, ],
       col = "red", lwd = 2, pch = 1)
points(depthSpace[(n + 1):(2 * n), ],
       col = "blue", lwd = 2, pch = 3)