Object embedding using an information geometrical perspective

Acquiring vector representations of objects is essential for applying machine learning, statistical inference, and visualization. Although various vector acquisition methods have been proposed considering the relationship between objects in target data, most of them are supposed to use only a specific relevance level. In real-world data, however, there are cases where multiple relationships are contained between objects, such as time-varying similarity in time-series data or various weighted edges on graph-structured data. In this paper, a vector acquisition method which assigns vectors in a single coordinate system to objects preserving the information given by multiple relations between objects is proposed. In the proposed method, a logarithmic bilinear model parameterized by representation vectors is utilized for approximating relations between objects based on a stochastic embedding idea. The inference algorithm proposed in this study is interpreted in terms of information geometry: the m-projection from the probability distribution constructed from observed relations on the model manifold and the e-mixture in the model manifold are alternately repeated to estimate the parameters. Finally, the performance of the proposed method is evaluated using artificial data, and a case study is conducted using real data.