# https://stackoverflow.com/questions/35194048/using-r-how-to-calculate #-the-distance-from-one-point-to-a-line # http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html # Kimberling, C. "Triangle Centers and Central Triangles." Congr. # Numer. 129, 1-295, 1998. .dist2d <- function(a, b, c) { v1 <- b - c v2 <- a - b m <- cbind(v1, v2) d <- abs(det(m)) / sqrt(sum(v1 * v1)) return(d) } .secondDerivativeEstimate <- function(v) { nv <- length(v) res <- rep(NA, nv) for (i in seq(2, nv - 1)) { res[i] <- v[i + 1] + v[i - 1] - (2 * v[i]) } return(res) } .curveElbow <- function(var, perplexity, pvalCutoff = 0.05) { len <- length(perplexity) a <- c(var[1], perplexity[1]) b <- c(var[len], perplexity[len]) res <- rep(NA, len) for (i in seq_along(var)) { res[i] <- .dist2d(c(var[i], perplexity[i]), a, b) } elbow <- which.max(res) ix <- var > var[elbow] perplexitySde <- .secondDerivativeEstimate(perplexity) perplexitySdeSd <- stats::sd(perplexitySde[ix], na.rm = TRUE) perplexitySdeMean <- mean(perplexitySde[ix], na.rm = TRUE) perplexitySdePval <- stats::pnorm(perplexitySde, mean = perplexitySdeMean, sd = perplexitySdeSd, lower.tail = FALSE) # other <- which(ix & perplexitySdePval < pvalCutoff) return(list(elbow = var[elbow])) }