Reconstruction of Distance Matrixes and their Aplication
Distance matrix are used in geometric modeling and in the restoration of geometric objects, economics, bioinformatics, and programming. Distance matrices are used in machine learning, for example, programs related to road traffic, bus routes, and geolocation. In particular, Yandex has created a serv...
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| Date: | 2021 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Кам'янець-Подільський національний університет імені Івана Огієнка
2021
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| Online Access: | http://mcm-math.kpnu.edu.ua/article/view/251168 |
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| Journal Title: | Mathematical and computer modelling. Series: Physical and mathematical sciences |
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Mathematical and computer modelling. Series: Physical and mathematical sciences| Summary: | Distance matrix are used in geometric modeling and in the restoration of geometric objects, economics, bioinformatics, and programming. Distance matrices are used in machine learning, for example, programs related to road traffic, bus routes, and geolocation. In particular, Yandex has created a service in which distance matrices predict road congestion at the right time in the future. In this way, motorists can prevent traffic jams. Distance matrices can also be used to create any statistics. In bioinformatics, distance matrices are used to represent protein structures in a coordinate-independent manner, or to reconstruct distances in the DNA chain. Distance Matrix API is a service that provides distance and time for the exit and destination matrix. The API returns information based on the suggested route between the start and end points calculated by the Google Maps API and consists of paths that include duration and distance values for each pair.
In [4] authors reviews the fundamental properties of EDMs, such as rank or (non)definiteness. Authors shows how various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, authors demonstrates applications to microphone position calibration, ultrasound tomography.
The paper finds a criterion for the possibility of restoring the matrix of Euclidean distances on a line and between the vertices of a convex n-gon on a plane. An algorithm for transferring a key to a cipher using Euclidean distance matrices on a plane has been developed. A fast algorithm for reconstructing the distance matrixes between objects on a straight line has been developed. |
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