{"title":"Clustering and Geodesic Scaling of Dissimilarities on the Spherical Surface","authors":"","doi":"10.1007/s13253-023-00597-4","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>Spherical embedding is an important tool in several fields of data analysis, including environmental data, spatial statistics, text mining, gene expression analysis, medical research and, in general, areas in which the geodesic distance is a relevant factor. Many data acquisition technologies are related to massive data acquisition, and these high-dimensional vectors are often normalised and transformed into spherical data. In this representation of data on spherical surfaces, multidimensional scaling plays an important role. Traditionally, the methods of clustering and representation have been combined, since the precision of the representation tends to decrease when a large number of objects are involved, which makes interpretation difficult. In this paper, we present a model that partitions objects into classes while simultaneously representing the cluster centres on a spherical surface based on geodesic distances. The model combines a partition algorithm based on the approximation of dissimilarities to geodesic distances with a representation procedure for geodesic distances. In this process, the dissimilarities are transformed in order to optimise the radius of the sphere. The efficiency of the procedure described is analysed by means of an extensive Monte Carlo experiment, and its usefulness is illustrated for real data sets. Supplementary material to this paper is provided online.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13253-023-00597-4","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Spherical embedding is an important tool in several fields of data analysis, including environmental data, spatial statistics, text mining, gene expression analysis, medical research and, in general, areas in which the geodesic distance is a relevant factor. Many data acquisition technologies are related to massive data acquisition, and these high-dimensional vectors are often normalised and transformed into spherical data. In this representation of data on spherical surfaces, multidimensional scaling plays an important role. Traditionally, the methods of clustering and representation have been combined, since the precision of the representation tends to decrease when a large number of objects are involved, which makes interpretation difficult. In this paper, we present a model that partitions objects into classes while simultaneously representing the cluster centres on a spherical surface based on geodesic distances. The model combines a partition algorithm based on the approximation of dissimilarities to geodesic distances with a representation procedure for geodesic distances. In this process, the dissimilarities are transformed in order to optimise the radius of the sphere. The efficiency of the procedure described is analysed by means of an extensive Monte Carlo experiment, and its usefulness is illustrated for real data sets. Supplementary material to this paper is provided online.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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