{"title":"信息学中离散数据点的连续描述:使用样条函数","authors":"Yu-xian Liu, R. Rousseau","doi":"10.1108/00012531211215204","DOIUrl":null,"url":null,"abstract":"Purpose – The paper aims to propose the use of spline functions for the description and visualization of discrete informetric data.Design/methodology/approach – Interpolating cubic splines: are interpolating functions (they pass through the given data points); are cubic, i.e. are polynomials of third degree; have first and second derivatives in the data points, implying that they connect data points in a smooth way; satisfy a best‐approximation property which tends to reduce curvature. These properties are illustrated in the paper using real citation data.Findings – The paper reveals that calculating splines yields a differentiable function that still captures small but real changes. It offers a middle way between connecting discrete data by line segments and providing an overall best‐fitting curve.Research limitations/implications – The major disadvantage of the use of splines is that accurate data are essential.Practical implications – Spline functions can be used for illustrative as well as modelling p...","PeriodicalId":55449,"journal":{"name":"Aslib Proceedings","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2012-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A continuous description of discrete data points in informetrics: Using spline functions\",\"authors\":\"Yu-xian Liu, R. Rousseau\",\"doi\":\"10.1108/00012531211215204\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Purpose – The paper aims to propose the use of spline functions for the description and visualization of discrete informetric data.Design/methodology/approach – Interpolating cubic splines: are interpolating functions (they pass through the given data points); are cubic, i.e. are polynomials of third degree; have first and second derivatives in the data points, implying that they connect data points in a smooth way; satisfy a best‐approximation property which tends to reduce curvature. These properties are illustrated in the paper using real citation data.Findings – The paper reveals that calculating splines yields a differentiable function that still captures small but real changes. It offers a middle way between connecting discrete data by line segments and providing an overall best‐fitting curve.Research limitations/implications – The major disadvantage of the use of splines is that accurate data are essential.Practical implications – Spline functions can be used for illustrative as well as modelling p...\",\"PeriodicalId\":55449,\"journal\":{\"name\":\"Aslib Proceedings\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Aslib Proceedings\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1108/00012531211215204\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aslib Proceedings","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1108/00012531211215204","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A continuous description of discrete data points in informetrics: Using spline functions
Purpose – The paper aims to propose the use of spline functions for the description and visualization of discrete informetric data.Design/methodology/approach – Interpolating cubic splines: are interpolating functions (they pass through the given data points); are cubic, i.e. are polynomials of third degree; have first and second derivatives in the data points, implying that they connect data points in a smooth way; satisfy a best‐approximation property which tends to reduce curvature. These properties are illustrated in the paper using real citation data.Findings – The paper reveals that calculating splines yields a differentiable function that still captures small but real changes. It offers a middle way between connecting discrete data by line segments and providing an overall best‐fitting curve.Research limitations/implications – The major disadvantage of the use of splines is that accurate data are essential.Practical implications – Spline functions can be used for illustrative as well as modelling p...