The Topology of Semantic Knowledge

Studies of the graph of dictionary definitions (DD) (Picard et al., 2009; Levary et al., 2012) have revealed strong semantic coherence of local topological structures. The techniques used in these papers are simple and the main results are found by understanding the structure of cycles in the directed graph (where words point to definitions). Based on our earlier work (Levary et al., 2012), we study a different class of word definitions, namely those of the Free Association (FA) dataset (Nelson et al., 2004). These are responses by subjects to a cue word, which are then summarized by a directed, free association graph. We find that the structure of this network is quite different from both the Wordnet and the dictionary networks. This difference can be explained by the very nature of free association as compared to the more “logical” construction of dictionaries. It thus sheds some (quantitative) light on the psychology of free association. In NLP, semantic groups or clusters are interesting for various applications such as word sense disambiguation. The FA graph is tighter than the DD graph, because of the large number of triangles. This also makes drift of meaning quite measurable so that FA graphs provide a quantitative measure of the semantic coherence of small groups of words.