Bidirectional Spatial Positioning of Concepts Using Neural Networks

Abstract

Spatial positioning of concepts on a plane or in 3-dimensional space is effective in understanding the relationship between them. In addition to the traditional principal component analysis, quantification theory and multidimensional scaling, various studies using neural networks have recently been carried out. Most of them aim at the positioning of concepts based on the similarity between them. However, resulting positioning does not necessarily coincide with that of a user.
Having applications to document retrieval in mind, the present paper determines the positioning of keywords on a plane by an optimization method called quantification theory 4. This positioning is modified reflecting an opinion of a user. This is followed by an inverse optimization method: the acquisition of the similarity between keywords which optimize the modified positioning. This is reduced to the maximization of the square of the cosine of the angle between an output vector and a target output vector. The learning of neural networks under constraints realizes this optimization. An application of this bidirectional positioning to small scale real data demonstrates its effectiveness.