Revisiting Probabilistic Relation Analysis: Using Probabilistic Relation Graphs for Relational Similarity Analysis of Words in Short Texts

Relation graphs provide useful tools for structural and relational analyses of highly complex multi-component systems. Probabilistic relation graph models can represent relations between system components by their probabilistic links. These graph types have been widely used for graphical representation of Markov models and bigram probabilities. This study presents an implication of relational similarities within probabilistic graph models of textual entries. The article discusses several utilization examples of two fundamental similarity measures in probabilistic analysis of short texts. To this end, construction of probabilistic graph models by using bigram probability matrices of textual entries is illustrated and vector spaces of input word-vectors and output word-vectors are formed. In this vector space, utilization of cosine similarity and mean squared error measures are demonstrated to evaluate probabilistic relational similarity between lexeme pairs in short texts. By using probabilistic relation graphs of the short texts, relational interchangeability analyses of lexeme pairs are conducted, and confidence index parameters are defined to express reliability of these analyses. Potential applications of these graphs in language processing and linguistics are discussed on the basis of the analysis results of example texts.