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Questions tagged [euclidean-distance]

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22 questions with no upvoted or accepted answers
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4 votes
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Finding the smallest distance between a point and a set of points

I have a GPS dataset that corresponds to a route taken by a vehicle in a day. It consist of a set of coordinates. Then say I have a coordinate and I want to know how close this coordinate is to this ...
TarsEndurance's user avatar
3 votes
0 answers
51 views

Distance from high dimensional convex hull to target point T

I have a set S of high dimensional points in Euclidean space, with convex hull H (not known); and some target point T in that space not in or on H. Rather than worry about calculating both H and the ...
jdowdell's user avatar
  • 131
3 votes
0 answers
446 views

Stable and fast computation of the squared euclidean distance matrix

Let's say I want to compute the matrix $M$ of the squared euclidean distances between each pair of vectors $(x, y)$ belonging to two sets $X$ and $Y$ respectively. The sets of vectors $X$ and $Y$ have ...
Celelibi's user avatar
  • 453
3 votes
0 answers
333 views

Sub-optimal and fast solutions to assignment problem

I am looking for a fast solution to the assignment problem for large cost matrices (5000x5000 or larger). The Hungarian algorithm is $O^3$, which is impractical for any moderately large problem. Are ...
Strabonio's user avatar
  • 131
3 votes
0 answers
170 views

Is it possible to simulate/emulate non-euclidean geometry using computer graphics?

I am aware of the frequent use of "smoke and mirrors" in order to achieve the effect of non-euclidean geometry, but I was wondering it if it possible to implement spherical (sometimes called elliptic) ...
Joe Carr's user avatar
  • 131
3 votes
0 answers
130 views

How fast is closest pair?

I'm reading a recent paper "Finding Correlations in Subquadratic Time, with Applications to Learning Parities and the Closest Pair Problem" by Gregory Valiant on finding approximate closest pairs in $...
Thomas Ahle's user avatar
2 votes
0 answers
145 views

Optimal Item Locations given Traversal Paths

I have a given fully-connected undirected graph associated with (known) distances or alternatively a distance matrix, where the nodes or matrix rows/columns represent locations. Additionally, I have a ...
aru_bdd's user avatar
  • 21
2 votes
0 answers
85 views

Mahalanobis distance of point to plane algorithm

I am trying to understand the Mahalanobis distance of a point from the plane given by this paper. The algorithm is given below: Calculate covariance of point $S_{uu}$ Apply a whitening transform to ...
shunyo's user avatar
  • 121
2 votes
0 answers
52 views

Finding multiple paths through a grid such that every grid square is equally used

Setup Here’s the setup: I have an $N$ x $N$ grid of tiles, and a list of $M$ agents that need to move across the grid. Each agent has its own start tile $S(a)$, end tile $E(a)$, and an exact number ...
Paul Accisano's user avatar
2 votes
0 answers
35 views

Efficient parameterization of low vertex count polygons

I'm trying to design a method to represent polygons as vectors. There are many ways to do this, but I have a few goals and I'm not sure what representation is best to fulfil these. The objectives are: ...
Erik's user avatar
  • 21
2 votes
0 answers
152 views

"Loneliest point" algorithm

Problem: I'm looking for an algorithm to find the maximal Euclidean distance between points in a set $R$ and another set $S \subseteq R$. Specifically, given a finite set of points $S$ in $n$-...
Michael Dunne's user avatar
2 votes
0 answers
31 views

Partial TSP in Euclidian plane

I'm interested in the following variant of Travelling Salesman Problem sometimes called Partial TSP. I'm particulary interested in the euclidian version : Input : A set $\{x_1,\dots,x_n\}\subset \...
Mathieu Mari's user avatar
1 vote
0 answers
24 views

Clustering 2D points with flavour

Problem Description I have two sets of 2D points with flavours: Noisy points $$p_i = (x_i, y_i, f_i) : p_i \in N : |N|\approx 10^8 $$ and true points $$p_{t_i} = (x_{t_i}, y_{t_i}, f_{t_i}) : p_{t_i} \...
Emil Jansson's user avatar
1 vote
0 answers
75 views

Can we make at most 3 comparisons in the closest points algorithm instead of 7?

Let's say I am using the divide and conquer algorithm outlined here, but I only want to return the minimum distance. I understand why that algorithm puts an upper-bound at 7 but I think that can be ...
Sam's user avatar
  • 11
1 vote
0 answers
53 views

Show that the local feature size is Lipschitz continuous

In class we defined "local features size" $\rho$ as follows: Let $C$ be a smooth closed curve in the plane, and let $x$ be a point of $C$. The local feature size $\rho(x)$ of $x$ is the ...
3nondatur's user avatar
  • 457
1 vote
0 answers
34 views

In multiobjective optimization, how to calculate the distance to reference point?

In multiobjective optimization, what does the distance exactly means, is it: 1) The distance from reference point (V) to an individual (Xi) (candidate solution) in the population (decision space). <...
shdotcom's user avatar
1 vote
0 answers
301 views

Total distance between points on a grid with time complexity lower than $O(n^2)$

I have $n$ points that form a grid with empty space and I need to find an algorithm that would calculate the total distance of those points with time complexity lower than $O(n^2)$. An example of a ...
Mike's user avatar
  • 11
1 vote
0 answers
16 views

Modifying the Erroneous Pairwise Distances of 4 Points to Get Coplanarity

Consider four points $i,j,k,l$ and their pairwise Euclidiean distances $d(ij)$ $d(ik)$ $d(il)$ $d(jk)$ $d(jl)$ $d(kl)$ Say that, we know the coordinates of the points $j$, $k$ and $l$. However, we ...
padawan's user avatar
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Does T5 or another embedding embed every possible length tokenization?

I’m curious about an embedding technique where every possible “tokenization” of a text gets an embedding - not just individuals words, but every single 2-gram, 3-gram, and n-gram. Does this exist? Or ...
Julius Hamilton's user avatar
0 votes
1 answer
243 views

Efficient Method for Distance Comparison in Euclidean Space

I have a vector of 2D Euclidean coordinates, and I need to find out if two or more points are within a distance threshold. The naive approach is to compare each point with every other point, but I am ...
disguisedtoast's user avatar
0 votes
0 answers
74 views

Euclidean space vs metric space in density clustering algorithms

I'm trying to find out if these algorithm still work if i replace the Euclidean space with metric space defined on the input point set. But i'm having some trouble figuring it out for some of them. I ...
FlubberBeer's user avatar
0 votes
0 answers
179 views

Clustering non-overlapping time series

I have thousands of times series of different length and different time. I want to group them together so that I know the optimal ones to pick as input for a ML algorithm and to document how they are ...
Al rl's user avatar
  • 101