Euclidean space

(redirected from Euclidean vector)
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Related to Euclidean vector: magnitude, Euclidean vector space
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Words related to Euclidean space

a space in which Euclid's axioms and definitions apply

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We present experiments with high-dimensional Euclidean vectors and gray-level images to compare vp-trees to mvp-trees to demonstrate the efficiency of mvp-trees.
We test a simple heuristic that chooses points that are far away from most of the data points for Euclidean vectors, and compare it to the results where the vantage points are chosen randomly.
In these experiments, Euclidean vectors are used to observe and compare the performance of mvp-trees with more than two vantage points in a node.
Two types of data, high-dimensional Euclidean vectors and gray-level MRI images (where each image has 256*256 pixels) were used for empirical study.
We used two sets of Euclidean vectors with two different distributions.
Our first set of experiments were conducted on uniformly distributed Euclidean vectors.
We initially tried randomly generated 20-dimensional Euclidean vectors, but the selectivity for the query ranges we tried was very low.
Another set of experiments were conducted on 20-dimensional Euclidean vectors generated in clusters of equal size.
p] distance between any two N-dimensional Euclidean vectors X and Y (denoted Dp(X, Y)) is calculated as follows:
When calculating distances, these images are simply treated as 256*256 = 65,536-dimensional Euclidean vectors, and the pixel by pixel intensity differences are accumulated using [L.