# Sample points on curves Samples points uniformly on curves interpolated as linear consequent segments. ```r sample.curves(curves, ptsPerCurve = as.integer(c(500))) ``` ## Arguments - `curves`: A list where each element is a function being a list containing a matrix `coords` (curves' values, d columns). - `ptsPerCurve`: A vector of numbers of points to be sampled on each curve. If `length(ptsPerCurve) < length(curves)` then the first entry of `ptsPerCurve` is considered only, and corresponds to the number of points on a curve. ## Returns A list of curves with each entry being a list constiting of [[1]] the drawn curve being a matrix named `coords`, [[2]] length of the curve as in `curves` named `length.init`, and [[3]] length of the drawn curve named `length`. ## Examples ```r 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]) set.seed(1) curves0Smpl <- sample.curves(curves0, 2 * m) curves1Smpl <- sample.curves(curves1, 2 * m) # Calculate depths depthSpace = matrix(NA, nrow = n * 2, ncol = 2) depthSpace[, 1] = depth.curve.Tukey( c(curves0Smpl, curves1Smpl), curves0Smpl, exactEst = TRUE, minMassObj = cst/m^alp) depthSpace[, 2] = depth.curve.Tukey( c(curves0Smpl, curves1Smpl), curves1Smpl, 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) ``` ## References Lafaye De Micheaux, P., Mozharovskyi, P. and Vimond, M. (2018). Depth for curve data and applications.

sample.curves function