# Mean-shift mode seeking algorithm Given a sample from a d-dimensional distribution, an initialization point and a bandwidth the algorithm finds the nearest mode of the corresponding Gaussian kernel density. ```r ms(X, init, H, tol = 1e-06, ncores = 1, store = FALSE) ``` ## Arguments - `X`: n by d matrix containing the data. - `init`: d-dimensional vector containing the initial point for the optimization. - `H`: Positive definite bandwidth matrix representing the covariance of each component of the Gaussian kernel density. - `tol`: Tolerance used to assess the convergence of the algorithm, which is stopped if the absolute values of increments along all the dimensions are smaller then tol at any iteration. Default value is 1e-6. - `ncores`: Number of cores used. The parallelization will take place only if OpenMP is supported. - `store`: If `FALSE` only the latest iteration is returned, if `TRUE` the function will return a matrix where the i-th row is the position of the algorithms at the i-th iteration. ## Returns A list where `estim` is a d-dimensional vector containing the last position of the algorithm, while `traj` is a matrix with d-colums representing the trajectory of the algorithm along each dimension. If `store == FALSE` the whole trajectory is not stored and `traj = NULL`. ## Examples ```r set.seed(434) # Simulating multivariate normal data N <- 1000 mu <- c(1, 2) sigma <- matrix(c(1, 0.5, 0.5, 1), 2, 2) X <- rmvn(N, mu = mu, sigma = sigma) # Plotting the true density function steps <- 100 range1 <- seq(min(X[ , 1]), max(X[ , 1]), length.out = steps) range2 <- seq(min(X[ , 2]), max(X[ , 2]), length.out = steps) grid <- expand.grid(range1, range2) vals <- dmvn(as.matrix(grid), mu, sigma) contour(z = matrix(vals, steps, steps), x = range1, y = range2, xlab = "X1", ylab = "X2") points(X[ , 1], X[ , 2], pch = '.') # Estimating the mode from "nrep" starting points nrep <- 10 index <- sample(1:N, nrep) for(ii in 1:nrep) { start <- X[index[ii], ] out <- ms(X, init = start, H = 0.1 * sigma, store = TRUE) lines(out$traj[ , 1], out$traj[ , 2], col = 2, lwd = 2) points(out$final[1], out$final[2], col = 4, pch = 3, lwd = 3) # Estimated mode (blue) points(start[1], start[2], col = 2, pch = 3, lwd = 3) # ii-th starting value } ``` ## Author(s) Matteo Fasiolo .

ms function