This article discusses three measures of distance: Earth Mover’s Distance (EMD) for image search, Word Mover’s Distance (WMD) for document retrieval, and Concept Mover’s Distance (CMD) for analyzing concepts within texts. The measures progress from tangible to abstract, impacting their analytical power. The CMD, utilizing an “ideal pseudo document,” distinguishes itself by presuming likeness analytically, rather than physically.
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Distance as a Measure of Difference
Introduction
This article discusses three measures of distance: (1) the Earth Mover’s Distance (EMD; Rubner et al., 1998); (2) the Word Mover’s Distance (WMD; Kusner et al., 2015); and (3) the Concept Mover’s Distance (CMD; Stoltz & Taylor, 2019). These measures build on one another to quantify difference between items, and this article will discuss both the distance measures themselves and the progression from one to the next.
Earth Mover’s Distance
The Earth Mover’s Distance (EMD) is a measure for improving image database search. It calculates the distance between pairs of images, indicating higher similarity with a lower EMD. The use of image “signatures” improves computational efficiency and allows for partial matches, making it a useful measure of image similarity.
Word Mover’s Distance
The Word Mover’s Distance (WMD) extends the EMD to document classification and retrieval. By representing each word from a document as a vector, the distance between two documents can be calculated by minimizing the distance each embedded word must travel to transform one document into another. The WMD is useful for measuring semantic distance in text data.
Concept Mover’s Distance
The Concept Mover’s Distance (CMD) assumes analytical value to measure similarity. It differentiates from the WMD by using an “ideal pseudo document” against which documents can be analyzed, capturing the structure of concepts well and being robust to document length and sparse terms. The CMD is useful when there is an existing theory to test.
Conclusion
The progression from EMD to WMD and CMD involves a layering of abstraction that must be considered when evaluating the meaning of difference, but each measure has its potential relative to the requirements of the task at hand.
References
Jaynes, Julian. 1976. The Origins of Consciousness in the Breakdown of the Bicameral Mind. Houghton Mifflin.
Kusner, M. J., Sun, Y., Kolkin, N. I., & Weinberger, K. Q. (2015). From Word Embeddings To Document Distances. Proceedings of the 32 Nd International Conference on Machine Learning. International Conference on Machine Learning, Lille, France.
Lakoff, George. (2002). Moral Politics: How Liberals and Conservatives Think. Chicago, IL: The University of Chicago Press.
Mikolov, T., Chen, K., Corrado, G., & Dean, J. (2013). Efficient Estimation of Word Representations in Vector Space. http://arxiv.org/abs/1301.3781
Rubner, Y., Tomasi, C., & Guibas, L. J. (1998). A metric for distributions with applications to image databases. Sixth International Conference on Computer Vision (IEEE Cat. №98CH36271), 59–66. https://doi.org/10.1109/ICCV.1998.710701
Stoltz, D. S., & Taylor, M. A. (2019). Concept Mover’s Distance: Measuring concept engagement via word embeddings in texts. Journal of Computational Social Science, 2(2), 293–313. https://doi.org/10.1007/s42001-019-00048-6
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