Gaussian Distributed Graph Constrained Multi-Modal Gaussian Process Latent Variable Model for Ordinal Labeled Data

Abstract

This paper proposes a Gaussian distributed graph constrained multimodal Gaussian process latent variable model for ordinal labeled data. Rating data that are used in various real-world applications such as product recommendation can represent user preferences, but the difference between adjacent ratings is often uncertain due to the user's ambiguity. In order to capture the relationships among multimodal data including rating data, consideration of the uncertainty is necessary. Therefore, by applying the Gaussian distribution to the rating data, we calculate distributed labels that implicitly include the uncertainty, and thus, the Gaussian distributed graph based on their similarities can be constructed. By introducing a constraint calculated based on the graph Laplacian of the Gaussian distributed graph into the objective function of the multi-modal Gaussian process latent variable model, we can achieve an effective latent space that can consider a label correlation while accounting for the uncertainty. This is the contribution of this paper. The effectiveness of the proposed method is verified by experiments using some open datasets.