Projections of Tropical Fermat-Weber Points
In the tropical projective torus, it is not guaranteed that the projection of a Fermat-Weber point of a given data set is a Fermat-Weber point of the projection of the data set. In this paper, we focus on the projection on the tropical triangle (the three-point tropical convex hull), and we develop...
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| creator | Ding, Weiyi Tang, Xiaoxian |
| description | In the tropical projective torus, it is not guaranteed that the projection of
a Fermat-Weber point of a given data set is a Fermat-Weber point of the
projection of the data set. In this paper, we focus on the projection on the
tropical triangle (the three-point tropical convex hull), and we develop one
algorithm (Algorithm 1) and its improved version (Algorithm 4), 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 R and test how it works with random data sets. The
experimental results show that, these algorithms can succeed with a much higher
probability than choosing the tropical triangle randomly, the succeed rate of
these two algorithms is stable while data sets are changing randomly, and
Algorithm 4 can output the results much faster than Algorithm 1 averagely. |
| doi_str_mv | 10.48550/arxiv.2108.10124 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2108_10124</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2108_10124</sourcerecordid><originalsourceid>FETCH-LOGICAL-a674-c301eb18d3a4f58c3f37a8007a65d1cc04928634cbf20afbcc09398dd4415fcb3</originalsourceid><addsrcrecordid>eNotzr0KwjAUhuEsDqJegJPdpfWkSdp0FPEPBB0KjuUkTSDSGkmL6N37O33wDh8PIVMKCZdCwALDw92TlIJMKNCUD8n8FPzF6N75axd5G5XB35zGJtqY0GIfn40yITp5d-27MRlYbDoz-e-IlJt1udrFh-N2v1oeYsxyHmsG1Cgqa4bcCqmZZTlKgBwzUVOtgRepzBjXyqaAVr1LwQpZ15xTYbViIzL73X611S24FsOz-qirr5q9AKnJPAg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Projections of Tropical Fermat-Weber Points</title><source>arXiv.org</source><creator>Ding, Weiyi ; Tang, Xiaoxian</creator><creatorcontrib>Ding, Weiyi ; Tang, Xiaoxian</creatorcontrib><description>In the tropical projective torus, it is not guaranteed that the projection of
a Fermat-Weber point of a given data set is a Fermat-Weber point of the
projection of the data set. In this paper, we focus on the projection on the
tropical triangle (the three-point tropical convex hull), and we develop one
algorithm (Algorithm 1) and its improved version (Algorithm 4), 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 R and test how it works with random data sets. The
experimental results show that, these algorithms can succeed with a much higher
probability than choosing the tropical triangle randomly, the succeed rate of
these two algorithms is stable while data sets are changing randomly, and
Algorithm 4 can output the results much faster than Algorithm 1 averagely.</description><identifier>DOI: 10.48550/arxiv.2108.10124</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2021-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2108.10124$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2108.10124$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Ding, Weiyi</creatorcontrib><creatorcontrib>Tang, Xiaoxian</creatorcontrib><title>Projections of Tropical Fermat-Weber Points</title><description>In the tropical projective torus, it is not guaranteed that the projection of
a Fermat-Weber point of a given data set is a Fermat-Weber point of the
projection of the data set. In this paper, we focus on the projection on the
tropical triangle (the three-point tropical convex hull), and we develop one
algorithm (Algorithm 1) and its improved version (Algorithm 4), 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 R and test how it works with random data sets. The
experimental results show that, these algorithms can succeed with a much higher
probability than choosing the tropical triangle randomly, the succeed rate of
these two algorithms is stable while data sets are changing randomly, and
Algorithm 4 can output the results much faster than Algorithm 1 averagely.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzr0KwjAUhuEsDqJegJPdpfWkSdp0FPEPBB0KjuUkTSDSGkmL6N37O33wDh8PIVMKCZdCwALDw92TlIJMKNCUD8n8FPzF6N75axd5G5XB35zGJtqY0GIfn40yITp5d-27MRlYbDoz-e-IlJt1udrFh-N2v1oeYsxyHmsG1Cgqa4bcCqmZZTlKgBwzUVOtgRepzBjXyqaAVr1LwQpZ15xTYbViIzL73X611S24FsOz-qirr5q9AKnJPAg</recordid><startdate>20210823</startdate><enddate>20210823</enddate><creator>Ding, Weiyi</creator><creator>Tang, Xiaoxian</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210823</creationdate><title>Projections of Tropical Fermat-Weber Points</title><author>Ding, Weiyi ; Tang, Xiaoxian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-c301eb18d3a4f58c3f37a8007a65d1cc04928634cbf20afbcc09398dd4415fcb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Ding, Weiyi</creatorcontrib><creatorcontrib>Tang, Xiaoxian</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ding, Weiyi</au><au>Tang, Xiaoxian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Projections of Tropical Fermat-Weber Points</atitle><date>2021-08-23</date><risdate>2021</risdate><abstract>In the tropical projective torus, it is not guaranteed that the projection of
a Fermat-Weber point of a given data set is a Fermat-Weber point of the
projection of the data set. In this paper, we focus on the projection on the
tropical triangle (the three-point tropical convex hull), and we develop one
algorithm (Algorithm 1) and its improved version (Algorithm 4), 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 R and test how it works with random data sets. The
experimental results show that, these algorithms can succeed with a much higher
probability than choosing the tropical triangle randomly, the succeed rate of
these two algorithms is stable while data sets are changing randomly, and
Algorithm 4 can output the results much faster than Algorithm 1 averagely.</abstract><doi>10.48550/arxiv.2108.10124</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | Projections of Tropical Fermat-Weber Points |
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