Topic Modeling: Measuring Scholarly Impact Using a Topical Lens

Abstract

Topic modeling is a well-received, unsupervised method that learns thematic structures from large document collections. Numerous algorithms for topic modeling have been proposed, and the results of those algorithms have been used to summarize, visualize, and explore the target document collections. In general, a topic modeling algorithm takes a document collection as input. It then discovers a set of salient themes that are discussed in the collection and the degree to which each document exhibits those topics. Scholarly communication has been an attractive application domain for topic modeling to complement existing methods for comparing entities of interest. In this chapter, we explain how to apply an open source topic modeling tool to conduct topic analysis on a set of scholarly publications. We also demonstrate how to use the results of topic modeling for bibliometric analysis.

Appendix: Normalization, Mapping, and Clustering Techniques Used by VOSviewer

In this appendix, we provide a more detailed description of the normalization, mapping, and clustering techniques used by VOSviewer.

1.1 Normalization

We first discuss the association strength normalization (Van Eck & Waltman, 2009) used by VOSviewer to normalize for differences between nodes in the number of edges they have to other nodes. Let aij denote the weight of the edge between nodes i and j, where aij = 0 if there is no edge between the two nodes. Since VOSviewer treats all networks as undirected, we always have aij = aji. The association strength normalization constructs a normalized network in which the weight of the edge between nodes i and j is given by

$$ {s}_{ij}=\frac{2m{a}_{ij}}{k_i{k}_j}, $$

(11.12)

where k _i (k _j ) denotes the total weight of all edges of node i (node j) and m denotes the total weight of all edges in the network. In mathematical terms,

$$ {k}_i={\displaystyle \sum_j{a}_{ij}} \mathrm{and} m=\frac{1}{2}{\displaystyle \sum_i{k}_i}. $$

(11.13)

We sometimes refer to s _ij as the similarity of nodes i and j. For an extensive discussion of the rationale of the association strength normalization, we refer to Van Eck and Waltman (2009).

1.2 Mapping

We now consider the VOS mapping technique used by VOSviewer to position the nodes in the network in a two-dimensional space. The VOS mapping technique minimizes the function

$$ V\left({\mathbf{x}}_1,\dots, {\mathbf{x}}_n\right)={\displaystyle \sum_{i<j}{s}_{ij}{\left\Vert {\mathbf{x}}_i-{\mathbf{x}}_j\right\Vert}^2} $$

(11.14)

subject to the constraint

$$ \frac{2}{n\left(n-1\right)}{\displaystyle \sum_{i<j}\left\Vert {\mathbf{x}}_i-{\mathbf{x}}_j\right\Vert }=1, $$

(11.15)

where n denotes the number of nodes in a network, x _i denotes the location of node i in a two-dimensional space, and ||x _i  − x _j || denotes the Euclidean distances between nodes i and j. VOSviewer uses a variant of the SMACOF algorithm (e.g., Borg & Groenen, 2005) to minimize (11.14) subject to (11.15). We refer to Van Eck et al. (2010) for a more extensive discussion of the VOS mapping technique, including a comparison with multidimensional scaling.

1.3 Clustering

Finally, we discuss the clustering technique used by VOSviewer. Nodes are assigned to clusters by maximizing the function

$$ V\left({c}_1,\dots, {c}_n\right)={\displaystyle \sum_{i<j}\delta \left({c}_i,{c}_j\right)\left({s}_{ij}-\gamma \right)} $$

(11.16)

where c _i denotes the cluster to which node i is assigned, δ(c _i , c _j ) denotes a function that equals 1 if c _i  = c _j and 0 otherwise, and γ denotes a resolution parameter that determines the level of detail of the clustering. The higher the value of γ, the larger the number of clusters that will be obtained. The function in (11.16) is a variant of the modularity function introduced by Newman and Girvan (2004) and Newman (2005) for clustering the nodes in a network. There is also an interesting mathematical relationship between on the one hand the problem of minimizing (11.14) subject to (11.15) and on the other hand the problem of maximizing (11.16). Because of this relationship, the mapping and clustering techniques used by VOSviewer constitute a unified approach to mapping and clustering the nodes in a network. We refer to Waltman et al. (2010) for more details. We further note that VOSviewer uses the recently introduced smart local moving algorithm (Waltman & Van Eck, 2013) to maximize (11.16).