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Repository of the University of Hasselt containing publications in the fields of statistics, computer science, information strategies and material from the Institute for behavioural sciences.
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1.
Introduction to Informetrics - Egghe, Leo; Rousseau, Ronald
The book deals with the following topics: informetrics, bibliometrics, scientometrics, descriptive statistics, probability, inferential statistics, sampling, multivariate statistics, operations research, linear programming, integer programming, shortest path algorithm, queueing theory, queuing theory, book circulation, fuzzy set, citation analysis, citation network, citation matrix, bibliographic coupling, co-citation analysis, JCR, Journal Citation Reports, obsolescence, aging, ageing, half-life, synchronous, diachronous, science policy, information production process, IPP, informetric law, success-breeds-success, law of Mandelbrot, law of Zipf, law of Lotka, law of Bradford, law of Leimkuhler, fractal, duality, concentration theory, 80/20 rule, law of Price, concentration measure, law of Pareto, growth, power law, exponential function.
2.
The power of power laws and an interpretation of Lotkaian informetric systems as self-similar fractals - Egghe, Leo
Power laws as defined in 1926 by A. Lotka are increasing in importance because they have been found valid in varied social networks including the Internet. In this article some unique properties of power laws are proven.
They are shown to characterize functions with the scalefree property (also called self-similarity property) as well as functions with the product property. Power laws have other desirable properties that are not shared by exponential laws, as we indicate in this paper. Specifically, Naranan (1970) proves the validity of Lotkas law based on the exponential growth of articles in journals and of the number of...
3.
Relations between the continuous and the discrete Lotka power function - Egghe, Leo
The discrete Lotka power function describes the number of sources (e.g., authors) with n=1, 2, 3, . . items (e.g., publications). As in econometrics, informetrics theory requires functions of a continuous variable j, replacing the discrete variable n. Now j represents item densities instead of number of items. The continuous Lotka power function describes the density of sources with item density j. The discrete Lotka function one obtains from data, obtained empirically; the continuous Lotka function is the one needed when one wants to apply Lotkaian informetrics, i.e., to determine properties that can be derived from the (continuous) model. It...
4.
Positive reinforcement and 3-dimensional informetrics - Egghe, Leo
We show that the composition of two information production processes (IPPs), where the items of the first IPP are the sources of the second, and where the ranks of the sources in the first IPP agree with the ranks of the sources in the second IPP, yields an IPP which is positively reinforced with respect to the first IPP. This means that the rank-frequency distribution of the composition is the composition of the rank-frequency distribution of the first IPP and an increasing function ?, which is explicitly calculable from the two IPPs distributions.
5.
Solution of a problem of Buckland on the influence of obsolescence on scattering - Egghe, Leo
In an old paper [M.K. Buckland. Are obsolescence and scattering related? Journal of Documentation 28 (3) (1972) 242-246] Buckland poses the question if certain types of obsolescence of scientific literature (in terms of age of citations) implies certain types of journal scattering (in terms of cited journals). This problem is reformulated in terms of one- and two-dimensional obsolescence and linked with one- and two-dimensional growth, the latter being studied by Naranan. Naranan shows that two-dimensional exponential growth (i.e. of the journals and of the articles in journals) implies Lotka''s law, a law belonging to two-dimensional informetrics and describing scattering of...
6.
The source-item coverage of the Lotka function - Egghe, Leo
The following problem has never been studied : Given A, the total number of items (e.g. articles) and T, the total number of sources (e.g. journals that contain these articles) (hence A>T), when is there a Lotka function.
7.
Zipfian and Lotkaian continuous concentration theory - Egghe, Leo
This paper studies concentration (i.e. inequality) aspects of the functions of Zipf and of Lotka. Since both functions are power laws (i.e. they are mathematically the same) it suffices to develop one concentration theory for power laws and apply it twice for the different interpretations of the laws of Zipf and Lotka. After a brief repetition of the functional relationships between Zipfs law and Lotkas law, we prove that Prices law of concentration is equivalent with Zipfs law. The major part of the paper is devoted to the development of continuous concentration theory, based on Lorenz curves. We calculate...
8.
An approach to similarity measurement of absence-presence data: the case that common zeros matter - Egghe, Leo; Rousseau, Ronald
Similarity between objects (documents, persons, answers to a questionnaire, etc.) is generally determined through relations between representations of these objects. In the case of binary representations the presence of a property (e.g. an index term) carries a weight of one, its absence a weight of zero. In many similarity studies common zeros are ignored. This situation is called the zero insensitive case. In this article, however, we study the zero sensitive case. Clearly, answers to binary questionnaires (yes-no, encoded as 1-0) are zero sensitive, as people who answer no to the same questions are more similar than those who give...
9.
A local hierarchy theory for acyclic digraphs - Egghe, Leo; Rousseau, Ronald
Local hierarchy theory focuses on direct links in acyclic digraphs. In- and out-degrees are used to determine the local hierarchical number for each vertex in the graph. Together, these local hierarchical numbers form a vector through which hierarchical properties are studied. The main tool, leading to a partial order of acyclic digraphs is a form of generalized Lorenz curve. Gini-like measures respecting this partial order can be derived. Local hierarchy theory is then the theory related to this particular partial order. Results have possible applications in administration and business organizational charts and in citation analysis. In the latter, a direct...
10.
The core of scientific subjects : an exact definition using concetration theory and fuzzy set theory. - Egghe, Leo; Rousseau, Ronald
Determining the core of a field's literature. i.e. its 'most important' sources, has been and still is an important problem in bibliomehics. In this article an exact definition of a core of a bibliography or a conglomerate is presented. The main ingredients for this definition are: fuzzy set theory, Lorenz curves and concentration measures. If one prefers a strict delineation, the fuzzy core can easily be defuzzified. The method we propose does not depend on the subjective notion of 'importance'. It is, moreover, completely reproducible. The method and the resulting core is also independent of the mathematical function (Lotka, Zipf,...
11.
Vector retrieval, fuzzy retrieval and the universal fuzzy IR surface for IR evaluation - Egghe, Leo
It is shown that vector information retrieval (IR) and general fuzzy IR uses two types of fuzzy set operations: the original "Zadeh minmax operations" and the so-called "probabilistic sum and algebraic product operations".
The universal IR surface, valid for classical 01 IR (i.e. where ordinary sets are used) and used in IR evaluation, is extended to and reproved for vector IR, using the probabilistic sum and algebraic product model. We also show (by counterexample) that, using the "Zadeh minmax" fuzzy model, yields a breakdown of this IR surface.
12.
A proposal to define a core of a scientific subject: A definition using concentration and fuzzy sets - Egghe, Leo; Rousseau, Ronald
Determining the core of a field"s literature, i.e. its "most important" sources, has been and still is an important problem in bibliometrics. In this article an exact definition of a core of a bibliography or a conglomerate is presented. The main ingredients for this definition are: fuzzy set theory, Lorenz curves and concentration measures. If one prefers a strict delineation, the fuzzy core can easily be defuzzified. The method we propose does not depend on the subjective notion of "importance". It is, moreover, completely reproducible. The method and the resulting core is also independent of the mathematical function (Lotka, Zipf,...
13.
A universal method of information retrieval evaluation: the - Egghe, Leo
The paper shows that the present evaluation methods in information retrieval (basically recall R and precision P and in some cases fallout F) lack universal comparability in the sense that their values depend on the generality of the IR problem. A solution is given by
using all "parts" of the database, including the non-relevant documents and also the notretrieved
documents. It turns out that the solution is given by introducing the measure M
being the fraction of the not-retrieved documents that are relevant (hence the "miss"
measure). We prove that - independent of the IR problem or of the IR action - the quadruple...
14.
How to measure own-group preference? A novel approach to a sociometric problem - Egghe, Leo; Rousseau, Ronald
In this article we present a precise definition of the notion "own-group preference" and characterize all functions capable of correctly measuring it. Examples of such functions are provided. The weighted Lorenz curve and the theory developed for it will be our main tools for reaching this goal. We further correct our earlier articles on this subject. In the context of own-language preference, Bookstein and Yitzhaki proposed the logarithm of the odds-ratio as an acceptable measure of own-group preference. We now present a general framework within which the concept of own-group preference, and its opposite, namely own-group aversion, can be precisely...
15.
Size-frequency and rank-frequency relations,power laws and exponential relations: a unified approach - Egghe, Leo; Rousseau, Ronald
Power laws, such as Zipf s law, and exponential relations, leading to straight lines in
logarithmic or semi-logarithmic scales, are presented in a unified setting. It is shown
that the class of size-frequency power laws is larger than the class of rank-frequency
power laws. Their ubiquity in all fields of science is illustrated.
16.
The Byline: Thoughts on the distribution of author ranks in multiauthored papers - Egghe, Leo; Liming, Liang; Rousseau, Ronald
We analyze the multi-authorship matrix M, defined as the matrix where a cell M(j,k) denotes the number of times authors with j publications are ranked as kth author of an article. We prove that if the distribution of the number of authors per paper follows a power law, then the author rank distribution is approximately equal to this power law (more precisely, equal in Landau's big 0 sense). We further determine the author rank distribution in the case authors can be characterized through a seed number, this is the probability of preceding a fixed author in the byline of an...
17.
A General Framework for Relative Impact Indicators / Cadre général pour les facteurs dimpact relatifs - Egghe, Leo; Rousseau, Ronald
This article brings the underlying structure of different relative indicators to the forefront. Special attention is given to the relative impact of a journal within a set of journals, a so-called meta-journal. Examples of relative impact factors are calculated for a group of information science, and for a group of management journals. Advantages of relative impact indicators are highlighted. These indicators are further studied in the context of regression analysis. Finally, it is shown that, compared to the Ramirez-Garcia-Del Rio renormalized impact factor, the relative impact factor is more sensitive to changes of relative contributions of journals within a journal...
18.
A measure for the cohesion of weighted networks - Egghe, Leo; Rousseau, Ronald
A generalization of both the Botafogo-Rivlin-Shneiderman compactness measure and the Wiener index is presented. These new measures for the cohesion of networks can be used in case a dissimilarity value is given between nodes in a network or a graph. It is illustrated how a set of weights between connected nodes can be transformed into a set of dissimilarity measures for all nodes. The new compactness measure for the cohesion of weighted graphs has several desirable properties related to the disjoint union of two networks. Finally, an example is presented of the calculation of the new compactness measures for a...
19.
Comparing partial and truncated conglomerates from a concentration theoretic point of view - Egghe, Leo; Rousseau, Ronald
When studying numerical properties of a population (technically: a conglomerate) it often happens that not all data are known. It might be that the total number of objects (persons) in the population is known, but that data on a number of them is missing. It even happens frequently that the total number of objects (N) is unknown. Referring to the population as sources and to the property under investigation as items or as the production, the whole dataset of this conglomerate can be represented as an N-vector. In this article N-vectors representing sources and their respective productions are studied from...
20.
Theory and experimentation on the most-recent-reference distribution - Egghe, Leo; Ravichandra Rao, Inna Kedage
The cumulative distribution of the age of the most-recent-reference distribution is the ldquodualrdquo variant of the first-citation distribution. The latter has been modelled in previous publications of different authors but the former one has not. This paper studies a model of this cumulative most-recent-reference distribution which is different from the first-citation distribution. This model is checked on JASIS and JACS data, with success. The model involves the determination of 3 parameters and is a transformation of the lognormal distribution. However we also show that the first-citation model (involving only 2 parameters and which is easier to handle), developed in an...
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