Introduction: Tracing the History of a Discipline Through Quantitative and Qualitative Analyses of Scientific Literature

Abstract

The chapters of this book are concerned with learning of the evolution of ideas (theories, concepts, methods, and application domains) and of the history of a discipline, by means of the temporal evolution of word occurrences in papers published by scientific journals. The work carried out for each of the areas involved in the project (philosophy, sociology, psychology, linguistics, statistics) pursued different objectives: to obtain a first overview of the relationship between time and contents in order to observe latent temporal patterns; to identify relevant keywords; to cluster keywords portraying similar temporal patterns; to identify latent dynamics of cluster keywords; and to identify relevant topics as groups of related words. The contributions identified and analysed the main subject matters that, at the time of publication, were considered relevant by mainstream journals and offer new viewpoints to read and understand the evolution of a discipline. The interdisciplinary debate triggered by this research work is innovative because quantitative methods for text analysis have been used in areas of human and social sciences, which are traditionally studied through qualitative approaches, and also represents a positive experience since new paths have been explored by pooling together the qualitative and quantitative research methods, traditions, and expertise of different disciplines.

Appendix

1.1.1 A Brief Overview on Correspondence Analysis

Correspondence Analysis (CA) is an Explorative Data Analysis (EDA) that has proven useful in studying the conjoint distribution of two (or more) categorical variables. CA portrays the existing structure of association between two (or more) variables by means of simple plots that position the categories of the variables on a plane.

The quantitative perspective adopted by the contributions of this volume are based on words and word counts, i.e. they are based on the observation of occurrences of relevant keywords over time. In this perspective, CA can be exploited to achieve a content mapping as it is useful to represent the system of relationships among years (e.g. volumes of the journals), among words (e.g. relevant keywords), and between years and words. Although CA is not able to describe all relevant linguistic features of a set of texts, it contributes to highlight latent patterns. For example, in our case, it makes it possible to verify whether the volumes of a journal expressed a clear temporal pattern in their main contents.

In the simplest version, CA works on a two-way contingency table in which the rows represent keywords (e.g. m word-types w₁, …, w_m) and columns represent the volumes of the journal (e.g. p time-points t₁, …, t_p). Each cell of this (lexical) contingency table represents the number n_ij of occurrences of the i-th keyword (the i-th row) in the volume published at the j-th time-point (the j-th column) (Table 1.1).

Table 1.1 Example of (lexical) contingency table words × time-points

CA provides the best simultaneous representation of row profiles and column profiles on each axis (and on each plane generated by a pair of axes). The purpose of the CA is to translate the similarities between categories (words and volumes) in a graph in which the most similar categories are placed in adjacent positions in the space defined by the Cartesian axes. If you look at the words, it is fairly intuitive to think that the similarity between two words depends on how much the occurrences in the two rows of the table “resemble each other”, that is, how similar they are in terms of presence, absence, or occurrence in the journal volumes: if two words tend to be used in the same volumes and with similar frequency, they have a similar profile over time. Two words with an identical profile will have no distance between them, that is, they will be represented on a graph as two overlapping points.

The intuitive notion of similarity between the profiles of two words w_i and w_k is translated into a distance (chi-square distance) that can be calculated for each pair of words:

${d}_{ik}^2=\sum \limits_{j=1}^p\frac{n}{n_{.j}}{\left(\frac{n_{ij}}{n_{i.}}-\frac{n_{kj}}{n_{k.}}\right)}^2$

All the reasoning can be repeated by taking into consideration the similarity between pairs of volumes and considering the profiles of the two columns. Two volumes of the journal (time-points t_j and t_k) resemble each other if they have a similar lexical profile, i.e. if they include the same words with a similar relative frequency (Fig. 1.1).

Fig. 1.1

Profiles in terms of relative frequencies and positions on the plane of three time-points

The distance between two time-points t_j and t_k is given as:

${d}_{jk}^2=\sum \limits_{i=1}^m\frac{n}{n_{i.}}{\left(\frac{n_{ij}}{n_{.j}}-\frac{n_{ik}}{n_{.k}}\right)}^2$

From another viewpoint, the rows and the columns of this matrix are considered as vectors, i.e. as points in a multidimensional space, and the distance between two vectors is measured through a weighted Euclidian distance that compares the corresponding lexical profiles taking into account the size of the subcorpora (volumes) at each time-point and the occurrences of each word in the corpus as a whole.

Following the calculation of the pairwise distance for words and for volumes, the next step is to transform the space generated by the original variables in a Euclidean space generated by new orthogonal variables (components or axes). The multidimensional space generated by the matrix is reduced to orthogonal dimensions (axes) that are displayed as Cartesian axes. The number of dimensions of this new space (i.e. the number of orthogonal axes) is equal to the number of linearly independent variables (rank of the matrix) that, in our context, is the number of time-points minus one (p − 1, more generally min(m, p) − 1).

The starting point of this transformation are the square matrix m × m which contains the pairwise distances between words and the square matrix p × p with the pairwise distances between volumes. The calculation of the coordinates of each axis is based on the singular value decomposition (SVD). The orthogonal factorial axes are sorted according to the amount of inertia collected (according to degree of association), i.e. they are in order of relevance: the first is the most important axis and the one which collects the highest portion of the information contained in the contingency table, the second axis is the one which collects the highest portion of information not explained by the first axis and so on. The Cartesian plane constructed with the first two factorial axes is the two-dimensional space which best represents the structure of association shown in the contingency table on a low-dimensional Euclidean space, and so on.

Unlike other analyses that move from the analysis of a matrix cases × variables, in CA the contingency table can be read in two ways: as m row vectors in the p-1 dimensions space generated by the columns, i.e. m words in the space of p time-points (volumes), and as p column vectors in the m-1 dimensions space generated by the rows, i.e. p time-points in the space of m words. From this observation, there is the immediate possibility to obtain two graphs separately: one with the words and one with the volumes. For the geometric properties of the two spaces (duality), the dimensions are the same and the two graphs overlap. This makes it possible to observe the system of relations between all the categories in play; although we must be very careful in the interpretation of the joint graphical representation of the two variables. In order to briefly summarize the elements for reading the graphs obtained from CA, we should remember that the position where a word or a volume is found assumes a role only in the globally created context of the graph, i.e. it doesn’t have any meaning by itself, but it does have meaning in comparison with the positions taken by all the other points found in the solution with respect to the barycentre at the origin of the axes. If two words are close on the graph, it means that they have similar profiles and, analogously, if two volumes are close they have similar lexical profiles. The mutual position assumed by a word and a volume cannot be evaluated in a direct manner and must be evaluated with reference to the positions assumed by all the other elements. In this sense, it is useful to use the quadrants of the Cartesian plane and, thanks to the axes, the proximity can be evaluated by taking into account the angle formed by the axes (the more similar the angle formed with the axes is, the more they can be considered associated). The words or the volumes that contributed the most to the solution and which, therefore, can be considered the most important in the reconstructed context of the graph, are those which are distant from the origin of the axes. The densification of modalities in an area of the graph that stands out from the rest as a cluster might be interpreted as a semantic area and for this purpose one often choses to partition into clusters. The clusters of words or volumes should be homogeneous as much as possible within the group and, as much as possible, heterogeneous within groups. In the analysis of the lexical contingency table, a cluster analysis based on the CA groups together the volumes based on the lexical similarity (which is usually also visible in terms of proximity of the points on the graph).

1.1.2 An Example

To understand the functioning of the CA, an application example of a very simplified fictional corpus might be useful. Suppose you have 11 texts that include the topics of a journal of the statistical field and constitute a small text corpus:

• text01 regression analysis; linear regression

• text02 regression model; linear and non-linear model

• text03 generalized linear model; parameter estimation

• text04 sampling methods; random sampling; survey design and sampling methods

• text05 survey design; finite populations

• text06 methods for sampling elusive populations

• text07 Normal distribution

• text08 z-scores and Normal distribution

• text09 Gamma distribution

• text10 p-value: Normal distribution and Gamma—exponential family

• text11 regression analysis; Normal distribution

There are 53 word-tokens and 25 word-types in the corpus. Taking into account only the words that are repeated at least twice, namely distribution (5 occurrences) and, linear, Normal, regression, and sampling (4), methods and model (3), analysis, design, Gamma, populations, and survey (2), we can construct a contingency table words × texts (Table 1.2), in which we see, for example, that the word survey was used once each by texts 04 and 05.

Table 1.2 Contingency table words × texts

The CA of the contingency table results in 10 factorial axes. The first two axes collect 55% of the information (explained inertia) and the first factorial plane is shown in Fig. 1.2.

Fig. 1.2

First plane of correspondence analysis. Visualization of texts (a) and of both texts and words with frequency ≥2 (b)

Figure 1.2 shows very well the three latent patterns present in the texts that refer to linear model (regression, analysis), sampling methods (survey design, populations), and distribution (Normal, Gamma). Texts 01, 02, and 03 can be found together in the area of linear model (second quadrant, upper left) while texts 07, 08, 09, and 10 in the area of distribution (third quadrant, bottom left). Text 11 is somewhere between linear models and distributions areas because it includes both topics. In the area of sampling methods (first quadrant, on the left), there are the texts 04, 05, and 06. It is interesting to note the conjunction and which is found near the origin of the axes because it has been used in different contexts (though slightly more often used by those who talked about distributions).