Clustering Co-occurrence Graph based on Transitivity

Word co-occurrences form a graph, regarding words as nodes and co-occurrence relations as branches. Thus, a co-occurrence graph can be constructed by co-occurrence relations in a corpus. This paper discusses a clustering method of the co-occurrence graph, the decomposition of the graph, from a graph-theoretical viewpoint. Since one of the applications for the clustering results is the ambiguity resolution, each output cluster is expected to have no ambiguity and be specialized in a single topic. We observed that a graph has no ambiguity if its branches representing co-occurrence relations are transitive. An algorithm to extract such graphs are proposed and its uniqueness of the output is discussed. The effectiveness of our m e t h o d is examined by an experiment using co-occurrence graph obtained from a 30M bytes corpus. 1 I n t r o d u c t i o n Clustering is t h e operation to group words by some criterion. Thesauri and synonym dictionaries are some of its manual examples. Automatic outputs can be used not only to revise them, but also to aid ambiguity resolution, an essential problem in natural language processing. For instance, the m e ~ i n g of an ambiguous word can be decided by e.xamln'i~g the duster it belongs to. Furthermore, clusters grouped according to topics have many application areas such as automatic document classification. The input in this paper is the word co-occurrence graph obta~ued from corpus. The output is its subgraphs with the condition that each subgraph is specialized in a topic. Many automatic clustering methods have been already proposed. Most of them are based on the statistical similarity between two words. Our approach is different; it is graph theoretical. We tried to find out the special structure in linguistic graph. Having a huge co-occurrence graph obtained from a corpus, we first tried to decompose it to analyze its graph structure using graph theoretical tools, such as maximum strongly connected components, or biconnected components. Although both tools decompose a graph into tightly connected subgraphs, these trials resulted in vain. The question arose; what must be taken into account to decompose the cooccurrence graph. 7 The answer is the ambiguity. Furthermore, we reached to the conclusion that the ambiguity can be explained in terms of intransitivity. This feature is developed into an algorithm for clustering. This paper is organized as follows. The following chapter describes the relationship between the transitivity in the graph and the ambiguity resolution. Chapter 3 shows the relationships between clustering and transitivity. Chapter 4 proposes and discusses an algorithm for clustering. Related work is resumed in Chapter 5. Our method is examined in Chapter 6 by some experiments. 2 W o r d A m b i g u i t y a n d T r a n s i t i v i t y Two words are said to co-occur when they frequently appear close to each other within texts. Regarding words as nodes and co-occurring re-