Salton's Cosine Research Articles

Production and impact of Brazilian papers in Library and Information Science journals (1986-2015)

This paper aims to carry out a diachronic analysis of Brazilian scientific productivity in the Library and Information Science field as indexed by the Scopus database for the period 1986-2015. We also analyze the main journals that publish Brazilian contributions, compare the impact of Brazilian production between papers published in Latin language journals and those in English, and identify the primary language of Brazilian papers and the main collaborating countries. We carried out a search on Brazilian scientific productivity in the analyzed field in the Scopus database for the studied period. Then, through a manual filter, we identified a corpus of 1,195 papers. Of the 90 journals identified, 26 journals were considered the main venues for Brazilian Library and Information Science research. These were grouped using multivariate cluster analysis. The main collaborating countries were grouped based on normalized values of co-authorship using Salton's cosine measure. Since 2006, Brazilian scientific production has experienced a similar growth tendency as the rest of the world. We observed that Brazilian journals, publishing in Portuguese, formed a cluster, while English and Spanish language journals clustered separately. We observed that papers published in English received on average more citations than those papers published in other languages.

Using character n-grams to match a list of publications to references in bibliographic databases

For research evaluation, publication lists need to be matched to entries in large bibliographic databases, such as Thomson Reuters Web of Science. This matching process is often done manually, making it very time consuming. This paper presents the use of character n-grams as automated indicator to inform and ease the manual matching process. The similarity of two references was identified by calculating Salton's cosine for their common character n-grams. As a complementary and confirmatory measure, Kondrak's Levenshtein distance score, based on the character n-grams, is used to re-measure the similarity of the top matches resulting from Salton's cosine. These automated matches were compared to results from completely manual matching. Incorrect matches were examined in depth and possible solutions suggested. This method was applied to two independent datasets, to validate the results and inferences drawn. For both datasets, the Salton's score based on character n-grams proves to be a useful indicator to distinguish between correct and incorrect matches. The suggested method is compared with a baseline which is based on word unigrams. Accuracy of the character and word based systems are 96.0 and 94.7 %, respectively. Despite a small difference in accuracy, we observed that the character based system provides more correct matches when the data contains abbreviations, mathematical expressions or erroneous text.

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

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. The...

New relations between similarity measures for vectors based on vector norms

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 m...

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

AbstractThe 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.

New relations between similarity measures for vectors based on vector norms

AbstractThe 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.

On the normalization and visualization of author co-citation data: Salton's Cosine versus the Jaccard index

The debate about which similarity measure one should use for the normalization in the case of Author Co-citation Analysis (ACA) is further complicated when one distinguishes between the symmetrical...

On the normalization and visualization of author co‐citation data: Salton's Cosine versus the Jaccard index

AbstractThe debate about which similarity measure one should use for the normalization in the case of Author Co‐citation Analysis (ACA) is further complicated when one distinguishes between the symmetrical co‐citation—or, more generally, co‐occurrence—matrix and the underlying asymmetrical citation—occurrence—matrix. In the Web environment, the approach of retrieving original citation data is often not feasible. In that case, one should use the Jaccard index, but preferentially after adding the number of total citations (i.e., occurrences) on the main diagonal. Unlike Salton's cosine and the Pearson correlation, the Jaccard index abstracts from the shape of the distributions and focuses only on the intersection and the sum of the two sets. Since the correlations in the co‐occurrence matrix may be spurious, this property of the Jaccard index can be considered as an advantage in this case.

Similarity measures, author cocitation analysis, and information theory

AbstractThe use of Pearson's correlation coefficient in Author Cocitation Analysis was compared with Salton's cosine measure in a number of recent contributions. Unlike the Pearson correlation, the cosine is insensitive to the number of zeros. However, one has the option of applying a logarithmic transformation in correlation analysis. Information calculus is based on both the logarithmic transformation and provides a non‐parametric statistics. Using this methodology, one can cluster a document set in a precise way and express the differences in terms of bits of information. The algorithm is explained and used on the data set, which was made the subject of this discussion.

Similarity measures in scientometric research: The Jaccard index versus Salton's cosine formula

It is shown that in most practical cases Salton's cosine formula yields a numerical value that is twice Jaccard's index.