## Abstract

In an earlier article published in this journal (“Concept Mover’s Distance”, 2019), we proposed a method for measuring concept engagement in texts that uses word embeddings to find the minimum cost necessary for words in an observed document to “travel” to words in a “pseudo-document” consisting only of words denoting a concept of interest. One potential limitation we noted is that, because words associated with opposing concepts will be located close to one another in the embedding space, documents will likely have similar closeness to starkly opposing concepts (e.g., “life” and “death”). Using aggregate vector differences between antonym pairs to extract a direction in the semantic space pointing toward a pole of the binary opposition (following “The Geometry of Culture,” *American Sociological Review*, 2019), we illustrate how CMD can be used to measure a document’s engagement with binary concepts.

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## Notes

- 1.
Which we could get by subtracting the cosine similarity between “bowling” and “rich” (\(-0.754\)) from the cosine similarity between “bowling” and “poor” (0.962), and dividing by two.

- 2.
See [20, pp. 296–9] and [11] for more detailed discussions of the underlying algorithm. Several teams have found computationally efficient methods of solving the transportation problem and our method now incorporates linear complexity relaxed word mover’s distance [2], as implemented in the text2vec package [19].

- 3.

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## Acknowledgements

A replication repository for this paper can be found at: https://github.com/Marshall-Soc/cmd_geometry.

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## Appendix: Procedures for deriving a semantic directions

### Appendix: Procedures for deriving a semantic directions

Deriving a semantic direction in an embedding space is a specific kind of relation extraction or induction. As such, there are many viable procedures one could use to find the pole of a binary concept in an embedding space. First, the simplest method would involve changing the order of operations used by Kozlowski et al. [10]: average the vectors for the words on each pole and then take the difference between these two averages. Arseniev-Koehler and Foster [1] refer to this method as the “Larsen method” following [13, p. 5]. Kozlowski et al. [10, p. 943 fn8] state that the Larsen method produced “nearly identical results” to theirs.

Second, Arseniev-Koehler and Foster [1] compare the Larsen method to one used in Bolukbasi et al. [3, pp. 42–43], which entails getting the vector offsets of antonym pairs through subtraction, then dividing the resulting vector by the Euclidean norm of the vector offset for those antonym pairs (see also [6]). Arseniev-Koehler and Foster find the results are similar, but the Larsen method was more accurate than this Bolukbasi method.

Third, Bolukbasi et al. [4] offer an additional method involving taking the difference between antonym pairs (they specifically use gendered terms), but then using principal component analysis to find a suitable aggregate from the resulting vector differences.

Finally, for exhaustiveness, there is another procedure which involves measuring individual target words’ associations with antonym pairs. This procedure does not, however, define a semantic direction against which any word could be compared and thus cannot be used directly with CMD. Caliskan et al. [5] incorporate this approach into a measure of gender bias in target terms, a technique they refer to as the Word-Embedding Association Test (WEAT). This entails first picking a target term, such as “wrench” or “boat.” Then one would take the mean of this target term’s distances to female-typed words—such as “girl,” “woman,” or “lady.” Next, one would take the mean of this same term’s distances to male-typed words, such as “boy,” “man,” and “gentleman.” Finally, the analyst subtracts the first mean from the second mean, to arrive at a single measure of how strongly associated this target term is to either side of the binary (see also [7]).

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Taylor, M.A., Stoltz, D.S. Integrating semantic directions with concept mover’s distance to measure binary concept engagement.
*J Comput Soc Sc* **4, **231–242 (2021). https://doi.org/10.1007/s42001-020-00075-8

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### Keywords

- Concept mover’s distance
- Geometry of culture
- Word embeddings
- Text analysis
- Cultural sociology
- Natural language processing