nearest-neighbor

I've successfully implemented a way to generate Voronoi diagrams in 2 dimensions using Fortune's method. But now I'm trying to use it for nearest neighbor queries for a point (which is not one of the original points used to generate the diagram). I keep seeing people saying that it can be done in O(lg n) time (and I believe them), but I can't find a description of how it's actually done. I'm familiar with binary searches, but I can't figure out a good criteria to guarantee that upper bound. I also figured maybe it could have to do with inserting the point into the diagram and updating

Suppose we have two sets of points A, B, and we want to find for every point in set A its nearest neighbor in set B. There are many good algorithms to find the nearest neighbor for one point. Is there some way to use the information we got for a_1, to more efficiently search for the nearest neighbor for a_2 or other points in the set? I am thinking something like: use triangular inequlity to get a interval for possible distance between every point in B and new point a_2, and sort the max and min of the intervals, and then I can search only the points in B which falls in the first interval.

I working on a project at the moment, where I have a point feature -- the point feature includes a 142 points -- and multiple polygon (around 10). I want to calculate the distance between every single point and the nearest polygon feature in R. My current approach is tedious and a bit long winded. I am currently planning to calculate the distance between every single point and every single polygon. For example, I would calculate the distance between the 142 points and Polygon A, the distance between the 142 points and Polygon B, the distance between 142 points and Polygon C, etc. Here is a

Matrix M is the signatures matrix, which is produced via Minhashing of the actual data, has documents as columns and words as rows. So a column represents a document. Now it says that every stripe ( b in number, r in length) has its columns hashed, so that a column falls in a bucket. If two columns fall in the same bucket, for >= 1 stripes, then they are potentially similar. So that means that I should create b hashtables and find b independent hash functions? Or just one is enough and every stripe sends its columns to the same collections of buckets (but wouldn't this cancel the stripes)?

I have built a hollow cube in MATLAB, I want to completely fill its volume with small cubes. Then I want to find a way to access these cubes and make paths through them, i.e if cube x is currently accessed, there should be a way to know what is its right, left, top, bottom, front, and back closest neighbors (closest neighbors= the cubes directly beside the current cube). I think we have 6 neighbors, because we have 6 different faces of the cube. By knowing the nearest cube at every direction, a path through the cubes can be defined as a series of steps (eg, right, left, left, top, right, front

I'm Trying to perform a K nearest neighbor search using spark. I have a RDD[Seq[Double]] and I'm planing to return a RDD[(Seq[Double],Seq[Seq[Double]])] with the actual row and a list of neighbors val out = data.map(row => { val neighbours = data.top(num = 3)(new Ordering[Seq[Double]] { override def compare(a:Seq[Double],b:Seq[Double]) = { euclideanDistance(a,row).compare(euclideanDistance(b,row))*(-1) } }) (row,neighbours.toSeq) }) And it Gives the following error on spark Submit 15/04/29 21:15:39 WARN TaskSetManager: Lost task 0.0 in stage 1.0 (TID 2, 192.168.1.7): org.apache.spark

I have two vectors with a few thousand points, but generalized here: A <- c(10, 20, 30, 40, 50) b <- c(13, 17, 20) How can I get the indicies of A that are nearest to b ? The expected outcome would be c(1, 2, 2) . I know that findInterval can only find the first occurrence, and not the nearest, and I'm aware that which.min(abs(b[2] - A)) is getting warmer, but I can't figure out how to vectorize it to work with long vectors of both A and b . You can just put your code in a sapply. I think this has the same speed as a for loop so isn't technically vectorized though: sapply(b,function(x)which

This is a question related to https://stats.stackexchange.com/questions/21572/how-to-plot-decision-boundary-of-a-k-nearest-neighbor-classifier-from-elements-o For completeness, here's the original example from that link: library(ElemStatLearn) require(class) x <- mixture.example$x g <- mixture.example$y xnew <- mixture.example$xnew mod15 <- knn(x, xnew, g, k=15, prob=TRUE) prob <- attr(mod15, "prob") prob <- ifelse(mod15=="1", prob, 1-prob) px1 <- mixture.example$px1 px2 <- mixture.example$px2 prob15 <- matrix(prob, length(px1), length(px2)) par(mar=rep(2,4)) contour(px1, px2, prob15, levels=0