Measuring Prerequisite Relations Among Concepts

Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 1668–1674, Lisbon, Portugal, 17-21 September 2015. c⃝2015 Association for Computational Linguistics. Measuring Prerequisite Relations Among Concepts Chen Liang † Zhaohui Wu‡ Wenyi Huang† C. Lee Giles† †Information Sciences and Technology ‡Computer Science and Engineering The Pennsylvania State University University Park, PA cul226@ist.psu.edu zzw109@psu.edu {wzh112,giles}@ist.psu.edu Abstract A prerequisite relation describes a basic relation among concepts in cognition, ed- ucation and other areas. However, as a se- mantic relation, it has not been well stud- ied in computational linguistics. We inves- tigate the problem of measuring prereq- uisite relations among concepts and pro- pose a simple link-based metric, namely reference distance (RefD), that effectively models the relation by measuring how dif- ferently two concepts refer to each other. Evaluations on two datasets that include seven domains show that our single metric based method outperforms existing super- vised learning based methods. 1 Introduction What should one know/learn before starting to learn a new area such as “deep learning”? A key for answering this question is to understand what a prerequisite is. A prerequisite is usually a con- cept or requirement before one can proceed to a following one. And the prerequisite relation exists as a natural dependency among concepts in cog- nitive processes when people learn, organize, ap- ply, and generate knowledge (Laurence and Mar- golis, 1999). While there has been serious effort in understanding prerequisite relations in learning and education (Bergan and Jeska, 1980; Ohland et al., 2004; Vuong et al., 2011), it has not been well studied as a semantic relation in computa- tional linguistics, where researchers focus more on lexical relations among lexical items (Miller, 1995) and fine-grained entity relations in knowl- edge bases (Mintz et al., 2009). Instead of treating it as a relation extraction or link prediction problem using traditional machine learning approaches (Talukdar and Cohen, 2012; Yang et al., 2015), we seek to better understand prerequisite relations from a perspective of cog- nitive semantics (Croft and Cruse, 2004). Par- tially motivated by the theory of frame seman- tics (Fillmore, 2006), or, to understand a concept, one needs to understand all the related concepts in its “frame”, we propose a metric that measures prerequisite relations based on a simple observa- tion of human learning. When learning concept A, if one needs to refer to concept B for a lot of A’s related concepts but not vice versa, B would more likely be a prerequisite of A than A of B. Specif- ically, we model a concept in a vector space using its related concepts and measure the prerequisite relation between two concepts by computing how differently the two’s related concepts refer to each other, or reference distance (RefD). Our simple metric RefD successfully reflects some properties of the prerequisite relation such as asymmetry and irreflexivity; and can be prop- erly implemented for various applications using different concept models. We present an imple- mentation of the metric using Wikipedia by lever- aging the links as reference …

Content truncated to 500 words