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  • × author_ss:"Egghe, L."
  1. Egghe, L.: ¬A universal method of information retrieval evaluation : the "missing" link M and the universal IR surface (2004) 0.02 
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    Abstract
    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 not-retrieved 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 (P,R,F,M) belongs to a universal IR surface, being the same for all IR-activities. This universality is then exploited by defining a new measure for evaluation in IR allowing for unbiased comparisons of all IR results. We also show that only using one, two or even three measures from the set {P,R,F,M} necessary leads to evaluation measures that are non-universal and hence not capable of comparing different IR situations.
    Date
    14. 8.2004 19:17:22
    Type
    a
  2. Egghe, L.: Untangling Herdan's law and Heaps' law : mathematical and informetric arguments (2007) 0.00 
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    Abstract
    Herdan's law in linguistics and Heaps' law in information retrieval are different formulations of the same phenomenon. Stated briefly and in linguistic terms they state that vocabularies' sizes are concave increasing power laws of texts' sizes. This study investigates these laws from a purely mathematical and informetric point of view. A general informetric argument shows that the problem of proving these laws is, in fact, ill-posed. Using the more general terminology of sources and items, the author shows by presenting exact formulas from Lotkaian informetrics that the total number T of sources is not only a function of the total number A of items, but is also a function of several parameters (e.g., the parameters occurring in Lotka's law). Consequently, it is shown that a fixed T(or A) value can lead to different possible A (respectively, T) values. Limiting the T(A)-variability to increasing samples (e.g., in a text as done in linguistics) the author then shows, in a purely mathematical way, that for large sample sizes T~ A**phi, where phi is a constant, phi < 1 but close to 1, hence roughly, Heaps' or Herdan's law can be proved without using any linguistic or informetric argument. The author also shows that for smaller samples, a is not a constant but essentially decreases as confirmed by practical examples. Finally, an exact informetric argument on random sampling in the items shows that, in most cases, T= T(A) is a concavely increasing function, in accordance with practical examples.
    Type
    a
  3. Egghe, L.: ¬A rationale for the Hirsch-index rank-order distribution and a comparison with the impact factor rank-order distribution (2009) 0.00 
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    Abstract
    We present a rationale for the Hirsch-index rank-order distribution and prove that it is a power law (hence a straight line in the log-log scale). This is confirmed by experimental data of Pyykkö and by data produced in this article on 206 mathematics journals. This distribution is of a completely different nature than the impact factor (IF) rank-order distribution which (as proved in a previous article) is S-shaped. This is also confirmed by our example. Only in the log-log scale of the h-index distribution do we notice a concave deviation of the straight line for higher ranks. This phenomenon is discussed.
    Type
    a
  4. Egghe, L.: Dynamic h-index : the Hirsch index in function of time (2007) 0.00 
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    Abstract
    When there are a group of articles and the present time is fixed we can determine the unique number h being the number of articles that received h or more citations while the other articles received a number of citations which is not larger than h. In this article, the time dependence of the h-index is determined. This is important to describe the expected career evolution of a scientist's work or of a journal's production in a fixed year.
    Type
    a
  5. Egghe, L.: New relations between similarity measures for vectors based on vector norms (2009) 0.00 
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    Abstract
    The well-known similarity measures Jaccard, Salton's cosine, Dice, and several related overlap measures for vectors are compared. While general relations are not possible to prove, we study these measures on the trajectories of the form [X]=a[Y], where a > 0 is a constant and [·] denotes the Euclidean norm of a vector. In this case, direct functional relations between these measures are proved. For Jaccard, we prove that it is a convexly increasing function of Salton's cosine measure, but always smaller than or equal to the latter, hereby explaining a curve, experimentally found by Leydesdorff. All the other measures have a linear relation with Salton's cosine, reducing even to equality, in case a = 1. Hence, for equally normed vectors (e.g., for normalized vectors) we, essentially, only have Jaccard's measure and Salton's cosine measure since all the other measures are equal to the latter.
    Type
    a
  6. Egghe, L.; Liang, L.; Rousseau, R.: ¬A relation between h-index and impact factor in the power-law model (2009) 0.00 
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    Abstract
    Using a power-law model, the two best-known topics in citation analysis, namely the impact factor and the Hirsch index, are unified into one relation (not a function). The validity of our model is, at least in a qualitative way, confirmed by real data.
    Type
    a
  7. Egghe, L.; Rousseau, R.: ¬The influence of publication delays on the observed aging distribution of scientific literature (2000) 0.00 
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    Abstract
    Observed aging curves are influenced by publication delays. In this article, we show how the 'undisturbed' aging function and the publication delay combine to give the observed aging function. This combination is performed by a mathematical operation known as convolution. Examples are given, such as the convolution of 2 Poisson distributions, 2 exponential distributions, a 2 lognormal distributions. A paradox is observed between theory and real data
    Type
    a
  8. Egghe, L.; Rousseau, R.: ¬An h-index weighted by citation impact (2008) 0.00 
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    Abstract
    An h-type index is proposed which depends on the obtained citations of articles belonging to the h-core. This weighted h-index, denoted as hw, is presented in a continuous setting and in a discrete one. It is shown that in a continuous setting the new index enjoys many good properties. In the discrete setting some small deviations from the ideal may occur.
    Type
    a
  9. Egghe, L.: ¬A noninformetric analysis of the relationship between citation age and journal productivity (2001) 0.00 
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    Abstract
    A problem, raised by Wallace (JASIS, 37,136-145,1986), on the relation between the journal's median citation age and its number of articles is studied. Leaving open the problem as such, we give a statistical explanation of this relationship, when replacing "median" by "mean" in Wallace's problem. The cloud of points, found by Wallace, is explained in this sense that the points are scattered over the area in first quadrant, limited by a curve of the form y=1 + E/x**2 where E is a constant. This curve is obtained by using the Central Limit Theorem in statistics and, hence, has no intrinsic informetric foundation. The article closes with some reflections on explanations of regularities in informetrics, based on statistical, probabilistic or informetric results, or on a combination thereof
    Type
    a
  10. Egghe, L.: Type/Token-Taken informetrics (2003) 0.00 
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    Abstract
    Type/Token-Taken informetrics is a new part of informetrics that studies the use of items rather than the items itself. Here, items are the objects that are produced by the sources (e.g., journals producing articles, authors producing papers, etc.). In linguistics a source is also called a type (e.g., a word), and an item a token (e.g., the use of words in texts). In informetrics, types that occur often, for example, in a database will also be requested often, for example, in information retrieval. The relative use of these occurrences will be higher than their relative occurrences itself; hence, the name Type/ Token-Taken informetrics. This article studies the frequency distribution of Type/Token-Taken informetrics, starting from the one of Type/Token informetrics (i.e., source-item relationships). We are also studying the average number my* of item uses in Type/Token-Taken informetrics and compare this with the classical average number my in Type/Token informetrics. We show that my* >= my always, and that my* is an increasing function of my. A method is presented to actually calculate my* from my, and a given a, which is the exponent in Lotka's frequency distribution of Type/Token informetrics. We leave open the problem of developing non-Lotkaian Type/TokenTaken informetrics.
    Type
    a
  11. Egghe, L.: Sampling and concentration values of incomplete bibliographies (2002) 0.00 
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    Abstract
    This article studies concentration aspects of bibliographies. More, in particular, we study the impact of incompleteness of such a bibliography on its concentration values (i.e., its degree of inequality of production of its sources). Incompleteness is modeled by sampling in the complete bibliography. The model is general enough to comprise truncation of a bibliography as well as a systematic sample on sources or items. In all cases we prove that the sampled bibliography (or incomplete one) has a higher concentration value than the complete one. These models, hence, shed some light on the measurement of production inequality in incomplete bibliographies.
    Type
    a
  12. Egghe, L.; Liang, L.; Rousseau, R.: Fundamental properties of rhythm sequences (2008) 0.00 
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    Abstract
    Fundamental mathematical properties of rhythm sequences are studied. In particular, a set of three axioms for valid rhythm indicators is proposed, and it is shown that the R-indicator satisfies only two out of three but that the R-indicator satisfies all three. This fills a critical, logical gap in the study of these indicator sequences. Matrices leading to a constant R-sequence are called baseline matrices. They are characterized as matrices with constant w-year diachronous impact factors. The relation with classical impact factors is clarified. Using regression analysis matrices with a rhythm sequence that is on average equal to 1 (smaller than 1, larger than 1) are characterized.
    Type
    a
  13. Egghe, L.: Empirical and combinatorial study of country occurrences in multi-authored papers (2006) 0.00 
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    Abstract
    Papers written by several authors can be classified according to the countries of the author affiliations. The empirical part of this paper consists of two datasets. One dataset consists of 1,035 papers retrieved via the search "pedagog*" in the years 2004 and 2005 (up to October) in Academic Search Elite which is a case where phi(m) = the number of papers with m =1, 2,3 ... authors is decreasing, hence most of the papers have a low number of authors. Here we find that #, m = the number of times a country occurs j times in a m-authored paper, j =1, ..., m-1 is decreasing and that # m, m is much higher than all the other #j, m values. The other dataset consists of 3,271 papers retrieved via the search "enzyme" in the year 2005 (up to October) in the same database which is a case of a non-decreasing phi(m): most papers have 3 or 4 authors and we even find many papers with a much higher number of authors. In this case we show again that # m, m is much higher than the other #j, m values but that #j, m is not decreasing anymore in j =1, ..., m-1, although #1, m is (apart from # m, m) the largest number amongst the #j,m. The combinatorial part gives a proof of the fact that #j,m decreases for j = 1, m-1, supposing that all cases are equally possible. This shows that the first dataset is more conform with this model than the second dataset. Explanations for these findings are given. From the data we also find the (we think: new) distribution of number of papers with n =1, 2,3,... countries (i.e. where there are n different countries involved amongst the m (a n) authors of a paper): a fast decreasing function e.g. as a power law with a very large Lotka exponent.
    Type
    a
  14. Egghe, L.; Ravichandra Rao, I.K.: ¬The influence of the broadness of a query of a topic on its h-index : models and examples of the h-index of n-grams (2008) 0.00 
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    Abstract
    The article studies the influence of the query formulation of a topic on its h-index. In order to generate pure random sets of documents, we used N-grams (N variable) to measure this influence: strings of zeros, truncated at the end. The used databases are WoS and Scopus. The formula h=T**1/alpha, proved in Egghe and Rousseau (2006) where T is the number of retrieved documents and is Lotka's exponent, is confirmed being a concavely increasing function of T. We also give a formula for the relation between h and N the length of the N-gram: h=D10**(-N/alpha) where D is a constant, a convexly decreasing function, which is found in our experiments. Nonlinear regression on h=T**1/alpha gives an estimation of , which can then be used to estimate the h-index of the entire database (Web of Science [WoS] and Scopus): h=S**1/alpha, , where S is the total number of documents in the database.
    Type
    a
  15. Egghe, L.; Rousseau, R.; Rousseau, S.: TOP-curves (2007) 0.00 
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    Abstract
    Several characteristics of classical Lorenz curves make them unsuitable for the study of a group of topperformers. TOP-curves, defined as a kind of mirror image of TIP-curves used in poverty studies, are shown to possess the properties necessary for adequate empirical ranking of various data arrays, based on the properties of the highest performers (i.e., the core). TOP-curves and essential TOP-curves, also introduced in this article, simultaneously represent the incidence, intensity, and inequality among the top. It is shown that TOPdominance partial order, introduced in this article, is stronger than Lorenz dominance order. In this way, this article contributes to the study of cores, a central issue in applied informetrics.
    Type
    a
  16. Egghe, L.: ¬The influence of transformations on the h-index and the g-index (2008) 0.00 
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    Abstract
    In a previous article, we introduced a general transformation on sources and one on items in an arbitrary information production process (IPP). In this article, we investigate the influence of these transformations on the h-index and on the g-index. General formulae that describe this influence are presented. These are applied to the case that the size-frequency function is Lotkaian (i.e., is a decreasing power function). We further show that the h-index of the transformed IPP belongs to the interval bounded by the two transformations of the h-index of the original IPP, and we also show that this property is not true for the g-index.
    Type
    a
  17. Egghe, L.; Ravichandra Rao, I.K.: Duality revisited : construction of fractional frequency distributions based on two dual Lotka laws (2002) 0.00 
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    Abstract
    Fractional frequency distributions of, for example, authors with a certain (fractional) number of papers are very irregular and, therefore, not easy to model or to explain. This article gives a first attempt to this by assuming two simple Lotka laws (with exponent 2): one for the number of authors with n papers (total count here) and one for the number of papers with n authors, n E N. Based an an earlier made convolution model of Egghe, interpreted and reworked now for discrete scores, we are able to produce theoretical fractional frequency distributions with only one parameter, which are in very close agreement with the practical ones as found in a large dataset produced earlier by Rao. The article also shows that (irregular) fractional frequency distributions are a consequence of Lotka's law, and are not examples of breakdowns of this famous historical law.
    Type
    a
  18. Egghe, L.: Mathematical theory of the h- and g-index in case of fractional counting of authorship (2008) 0.00 
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    Abstract
    This article studies the h-index (Hirsch index) and the g-index of authors, in case one counts authorship of the cited articles in a fractional way. There are two ways to do this: One counts the citations to these papers in a fractional way or one counts the ranks of the papers in a fractional way as credit for an author. In both cases, we define the fractional h- and g-indexes, and we present inequalities (both upper and lower bounds) between these fractional h- and g-indexes and their corresponding unweighted values (also involving, of course, the coauthorship distribution). Wherever applicable, examples and counterexamples are provided. In a concrete example (the publication citation list of the present author), we make explicit calculations of these fractional h- and g-indexes and show that they are not very different from the unweighted ones.
    Type
    a
  19. Egghe, L.: ¬A model for the size-frequency function of coauthor pairs (2008) 0.00 
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    Abstract
    Lotka's law was formulated to describe the number of authors with a certain number of publications. Empirical results (Morris & Goldstein, 2007) indicate that Lotka's law is also valid if one counts the number of publications of coauthor pairs. This article gives a simple model proving this to be true, with the same Lotka exponent, if the number of coauthored papers is proportional to the number of papers of the individual coauthors. Under the assumption that this number of coauthored papers is more than proportional to the number of papers of the individual authors (to be explained in the article), we can prove that the size-frequency function of coauthor pairs is Lotkaian with an exponent that is higher than that of the Lotka function of individual authors, a fact that is confirmed in experimental results.
    Type
    a
  20. Egghe, L.; Leydesdorff, L.: ¬The relation between Pearson's correlation coefficient r and Salton's cosine measure (2009) 0.00 
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    Abstract
    The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1-norm and the L2-norm of a vector. These different values yield a sheaf of increasingly straight lines which together form a cloud of points, being the investigated relation. The theoretical results are tested against the author co-citation relations among 24 informetricians for whom two matrices can be constructed, based on co-citations: the asymmetric occurrence matrix and the symmetric co-citation matrix. Both examples completely confirm the theoretical results. The results enable us to specify an algorithm that provides a threshold value for the cosine above which none of the corresponding Pearson correlations would be negative. Using this threshold value can be expected to optimize the visualization of the vector space.
    Type
    a

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