The decomposition of scientific literature into disciplinary and subdisciplinary structures is one of the core goals of scientometrics. How can we achieve a good decomposition? The ISI subject categories classify journals included in the Science Citation Index (SCI). The aggregated journal-journal citation matrix contained in the Journal Citation Reports can be aggregated on the basis of these categories. This leads to an asymmetrical matrix (citing versus cited) that is much more densely populated than the underlying matrix at the journal level. Exploratory factor analysis of the matrix of subject categories suggests a 14-factor solution. This solution could be interpreted as the disciplinary structure of science. The nested maps of science (corresponding to 14 factors, 172 categories, and 6,164 journals) are online at . Presumably, inaccuracies in the attribution of journals to the ISI subject categories average out so that the factor analysis reveals the main structures. The mapping of science could, therefore, be comprehensive and reliable on a large scale albeit imprecise in terms of the attribution of journals to the ISI subject categories. © 2009 Wiley Periodicals, Inc.

https://www.leydesdorff.net/map06/texts/map06.pdf

A global map of science based on the ISI subject categories

In scientometric research, the use of cooccurrence data is very common. In many cases, a similarity measure is employed to normalize the data. However, there is no consensus among researchers on which similarity measure is most appropriate for normalization purposes. In this article, we theoretically analyze the properties of similarity measures for cooccurrence data, focusing in particular on four well-known measures: the association strength, the cosine, the inclusion index, and the Jaccard index. We also study the behavior of these measures empirically. Our analysis reveals that there exist two fundamentally different types of similarity measures, namely, set-theoretic measures and probabilistic measures. The association strength is a probabilistic measure, while the cosine, the inclusion index, and the Jaccard index are set-theoretic measures. Both our theoretical and our empirical results indicate that cooccurrence data can best be normalized using a probabilistic measure. This provides strong support for the use of the association strength in scientometric research. © 2009 Wiley Periodicals, Inc.

How to normalize cooccurrence dataq An analysis of some well-known similarity measures

The ISI subject categories classify journals included in the Science Citation Index (SCI). The aggregated journal-journal citation matrix contained in the Journal Citation Reports can be aggregated on the basis of these categories. This leads to an asymmetrical transaction matrix (citing versus cited) which is much more densely populated than the underlying matrix at the journal level. Exploratory factor analysis leads us to opt for a fourteen-factor solution. This solution can easily be interpreted as the disciplinary structure of science. The nested maps of science (corresponding to 14 factors, 172 categories, and 6,164 journals) are brought online at this http URL An analysis of interdisciplinary relations is pursued at three levels of aggregation using the newly added ISI subject category of "Nanoscience & nanotechnology". The journal level provides the finer grained perspective. Errors in the attribution of journals to the ISI subject categories are averaged out so that the factor analysis can reveal the main structures. The mapping of science can, therefore, be comprehensive at the level of ISI subject categories.

A Global Map of Science Based on the ISI Subject Categories

Recommender systems use algorithms to provide users with product or service recommendations. Recently, these systems have been using machine learning algorithms from the field of artificial intelligence. However, choosing a suitable machine learning algorithm for a recommender system is difficult because of the number of algorithms described in the literature. Researchers and practitioners developing recommender systems are left with little information about the current approaches in algorithm usage. Moreover, the development of a recommender system using a machine learning algorithm often has problems and open questions that must be evaluated, so software engineers know where to focus research efforts. This paper presents a systematic review of the literature that analyzes the use of machine learning algorithms in recommender systems and identifies research opportunities for software engineering research. The study concludes that Bayesian and decision tree algorithms are widely used in recommender systems because of their relative simplicity, and that requirement and design phases of recommender system development appear to offer opportunities for further research.

The Use of Machine Learning Algorithms in Recommender Systems: A Systematic Review

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. © 2009 Wiley Periodicals, Inc.

The relation between Pearson's correlation coefficient r and Salton's cosine measure

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 $||\overrightarrow X || = a||\overrightarrow Y ||$, 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. © 2009 Wiley Periodicals, Inc.

New relations between similarity measures for vectors based on vector norms

Similarity measures, such as the ones of Jaccard, Dice, or Cosine, measure the similarity between two vectors. A good property for similarity measures would be that, if we add a constant vector to both vectors, then the similarity must increase. We show that Dice and Jaccard satisfy this property while Cosine and both overlap measures do not. Adding a constant vector is called, in Lorenz concentration theory, “nominal increase” and we show that the stronger “transfer principle” is not a required good property for similarity measures. Another good property is that, when we have two vectors and if we add one of these vectors to both vectors, then the similarity must increase. Now Dice, Jaccard, Cosine, and one of the overlap measures satisfy this property, while the other overlap measure does not. Also a variant of this latter property is studied. © 2010 Wiley Periodicals, Inc.

Good properties of similarity measures and their complementarity

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 $\vec {X} \cdot \vec {Y} = a$, 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. © 2010 Wiley Periodicals, Inc.

On the relation between the association strength and other similarity measures

information retrieval; overlap studies; presence-absence data; Jaccard coefficient; Salton's cosine measure; Dice coefficient; Lorenz curves; Gini index

Classical retrieval and overlap measures such as Jaccard's coefficient, Salton's cosine measure and the Dice coefficient satisfy the requirements for rankings based upon a Lorenz curve.

Leo Egghe

Papers

The relation between Pearson's correlation coefficient r and Salton's cosine measure

New relations between similarity measures for vectors based on vector norms

Good properties of similarity measures and their complementarity

On the relation between the association strength and other similarity measures

Classical retrieval and overlap measures such as Jaccard's coefficient, Salton's cosine measure and the Dice coefficient satisfy the requirements for rankings based upon a Lorenz curve.