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Projections of Tropical Fermat-Weber Points
| Content Provider | MDPI |
|---|---|
| Author | Ding, Weiyi Tang, Xiaoxian |
| Copyright Year | 2021 |
| Description | This paper is motivated by the difference between the classical principal component analysis (PCA) in a Euclidean space and the tropical PCA in a tropical projective torus as follows. In Euclidean space, the projection of the mean point of a given data set on the principle component is the mean point of the projection of the data set. However, in tropical projective torus, it is not guaranteed that the projection of a Fermat-Weber point of a given data set on a tropical polytope is a Fermat-Weber point of the projection of the data set. This is caused by the difference between the Euclidean metric and the tropical metric. In this paper, we focus on the projection on the tropical triangle (the three-point tropical convex hull), and we develop one algorithm and its improved version, such that for a given data set in the tropical projective torus, these algorithms output a tropical triangle, on which the projection of a Fermat-Weber point of the data set is a Fermat-Weber point of the projection of the data set. We implement these algorithms in |
| Starting Page | 3102 |
| e-ISSN | 22277390 |
| DOI | 10.3390/math9233102 |
| Journal | Mathematics |
| Issue Number | 23 |
| Volume Number | 9 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2021-12-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Artificial Intelligence Fermat-weber Point Convex Polytope Tropical Projection Tropical Pca |
| Content Type | Text |
| Resource Type | Article |
