Search (59 results, page 1 of 3)

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Abstract

It is shown that a normalized version of the g-index is a good normalized impact and concentration measure. A proposal for such a measure by Bartolucci is improved.

Object

g-index

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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.

Object

g-index

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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.

Object

g-index

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Abstract

The author presents a different view on properties of impact measures than given in the paper of De Visscher (2011). He argues that a good impact measure works better when citations are concentrated rather than spread out over articles. The author also presents theoretical evidence that the g-index and the R-index can be close to the square root of the total number of citations, whereas this is not the case for the A-index. Here the author confirms an assertion of De Visscher.

Object

g-index

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Abstract

This paper studies mathematical properties of h-index sequences as developed by Liang [Liang, L. (2006). h-Index sequence and h-index matrix: Constructions and applications. Scientometrics, 69(1), 153-159]. For practical reasons, Liming studies such sequences where the time goes backwards while it is more logical to use the time going forward (real career periods). Both type of h-index sequences are studied here and their interrelations are revealed. We show cases where these sequences are convex, linear and concave. We also show that, when one of the sequences is convex then the other one is concave, showing that the reverse-time sequence, in general, cannot be used to derive similar properties of the (difficult to obtain) forward time sequence. We show that both sequences are the same if and only if the author produces the same number of papers per year. If the author produces an increasing number of papers per year, then Liang's h-sequences are above the "normal" ones. All these results are also valid for g- and R-sequences. The results are confirmed by the h-, g- and R-sequences (forward and reverse time) of the author.

Type

a

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Abstract

One aim of science evaluation studies is to determine quantitatively the contribution of different players (authors, departments, countries) to the whole system. This information is then used to study the evolution of the system, for instance to gauge the results of special national or international programs. Taking articles as our basic data, we want to determine the exact relative contribution of each coauthor or each country. These numbers are brought together to obtain country scores, or department scores, etc. It turns out, as we will show in this article, that different scoring methods can yield totally different rankings. Conseqeuntly, a ranking between countries, universities, research groups or authors, based on one particular accrediting methods does not contain an absolute truth about their relative importance

Type

a

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Date

14. 2.2012 12:53:22

Type

a

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Abstract

It is possible, using ISI's Journal Citation Report (JCR), to calculate average impact factors (AIF) for LCR's subject categories but it can be more useful to know the global Impact Factor (GIF) of a subject category and compare the 2 values. Reports results of a study to compare the relationships between AIFs and GIFs of subjects, based on the particular case of the average impact factor of a subfield versus the impact factor of this subfield as a whole, the difference being studied between an average of quotients, denoted as AQ, and a global average, obtained as a quotient of averages, and denoted as GQ. In the case of impact factors, AQ becomes the average impact factor of a field, and GQ becomes its global impact factor. Discusses a number of applications of this technique in the context of informetrics and scientometrics

Source

Journal of information science. 22(1996) no.3, S.165-170

Type

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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

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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

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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

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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.

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Abstract

Let (DS, DQ, sim) be a retrieval system consisting of a document space DS, a query space QS, and a function sim, expressing the similarity between a document and a query. Following D.M. Everett and S.C. Cater (1992), we introduce topologies on the document space. These topologies are generated by the similarity function sim and the query space QS. 3 topologies will be studied: the retrieval topology, the similarity topology and the (pseudo-)metric one. It is shown that the retrieval topology is the coarsest of the three, while the (pseudo-)metric is the strongest. These 3 topologies are generally different, reflecting distinct topological aspects of information retrieval. We present necessary and sufficient conditions for these topological aspects to be equal

Type

a

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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

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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

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Abstract

A graph in van Eck and Waltman [JASIST, 60(8), 2009, p. 1644], representing the relation between the association strength and the cosine, is partially explained as a sheaf of parabolas, each parabola being the functional relation between these similarity measures on the trajectories x*y=a, a constant. Based on earlier obtained relations between cosine and other similarity measures (e.g., Jaccard index), we can prove new relations between the association strength and these other measures.

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Abstract

We present a model that describes which fraction of the literature on a certain topic we will find when we use n (n = 1, 2, .) databases. It is a generalization of the theory of discovering usability problems. We prove that, in all practical cases, this fraction is a concave function of n, the number of used databases, thereby explaining some graphs that exist in the literature. We also study limiting features of this fraction for n very high and we characterize the case that we find all literature on a certain topic for n high enough.

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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