# Mean-shift mode seeking algorithm

### Description

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.

### Usage

1 |

### Arguments

`X` |
n by d matrix containing the data. |

`init` |
d-dimensional vector containing the initial point for the optimization. By default
it is equal to |

`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 |

### Value

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`

.

### Author(s)

Matteo Fasiolo <matteo.fasiolo@gmail.com>.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ```
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
}
``` |