Questions tagged [euclidean-distance]

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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 ...
49 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 ...
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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 ...
• 423
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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) ...
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1 vote
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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 ...
• 11
1 vote
32 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 ...
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1 vote
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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). <...
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1 vote
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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 ...
• 11
1 vote
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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 ...
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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 ...
22 views

Is it possible to approximate the cosine similarity by dot products?

My goal is to find an approximate way to calculate the cosine similarity by inner products. Before the question look at the image below taken from Improved Asymmetric Locality Sensitive Hashing (ALSH) ...
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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 ...
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Scaling down a set of points into a smaller area

A visibility graph $G(P) = (V,E)$ of a set $P = \{p_1, \dots, p_n\}$ of points is defined as follows. Each vertex $u \in V$ corresponds to a point $p_u \in P$. There exists an edge $uv \in E$ if, and ...
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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 ...
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