Given a point cloud
X (n points), The function
knnDE computes the k Nearest Neighbors Density Estimator over a grid of points. For each x \in R^d, the knn Density Estimator is defined by
p_X (x) = k / (n * v_d * r_k^d(x)),
where v_n is the volume of the Euclidean d dimensional unit ball and r_k^d(x) is the Euclidean distance from point x to its k'th closest neighbor.
an n by d matrix of coordinates of points used in the density estimation process, where n is the number of points and d is the dimension.
an m by d matrix of coordinates, where m is the number of points in the grid.
number: the smoothing paramter of the k Nearest Neighbors Density Estimator.
knnDE returns a vector of length m (the number of points in the grid) containing the value of the knn Density Estimator for each point in the grid.
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## Generate Data from the unit circle n <- 300 X <- circleUnif(n) ## Construct a grid of points over which we evaluate the function by <- 0.065 Xseq <- seq(-1.6, 1.6, by = by) Yseq <- seq(-1.7, 1.7, by = by) Grid <- expand.grid(Xseq, Yseq) ## kernel density estimator k <- 50 KNN <- knnDE(X, Grid, k)
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