A continuous description of discrete data points in informetrics

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 purposes. Originality/value -Splines have hardly ever been used or studied in the information sciences.

Citation analysis and the development of science: A case study using articles by some Nobel prize winners

“…Moreover, Egghe (, p. 19) writes that “a real powerful Lotkaian informetrics theory can only be produced in a continuous setting.” We claim that this is not only true for power laws (so‐called Lotkaian theory) but even more so for data that cannot easily be described by a simple continuous function. In previous publications (Liu & Rousseau, , 2012a) we have put forward arguments in favor of the use of spline functions. For this reason, we do not go into a discussion of whether splines, other continuous functions, or discrete finite differences are best.…”

“…Liu and Rousseau (2012a) have shown that using splines yields a differentiable function that still captures small but real changes. In this publication, we use splines to establish a function to depict academic movement as a time‐dependent dynamic process.…”

“…How then can such a function be constructed? We have illustrated that spline‐fitted data have the ability to approximate discrete data continuously and still capture small but real changes (see Liu & Rousseau, , 2012a). When data are given as a time series, a continuous function of cumulated citations with respect to time is established.…”

“…However, in an earlier article we noted that the term time series can cover many types and pointed out their differences (Liu & Rousseau, ). Another step is the realization that the knowledge production chain occurs through integration and diffusion (Carley & Porter, ; Gao & Guan, ; Leydesdorff & Rafols, ; Liu Rafols, & Rousseau, 2012; Porter, Cohen, Roessner, & Perrault, ; Rafols & Meyer, , ). New knowledge in a scientific publication is always based on, and to some extent derived from, existing bodies of knowledge.…”

“…Claim (1) has already been developed in an article about the work of Nobelist Charles Kuen Kao (Liu & Rousseau, 2012b), and the use of splines in the field of informetrics has been highlighted also (Liu & Rousseau, 2012a). In this contribution, Claim (1) is taken up again—with new examples—and extended to elaborate Claims (2) and (3).…”