Multidimensional Unfolding Based on Stochastic Neighbor Relationship

Multi-dimensional Unfolding (MU) is a method to visualize relevance data between two sets (e.g., preference data) as a single scatter plot. Usually, in the analysis of relevance data, users are interested in which elements are strongly related to each other (e.g., how much an individual likes an item), and not in which elements are irrelevant to each other. However, the conventional MU often suffers from the problem that relationships between irrelevant pairs are overly emphasized and those between relevant pairs are not represented appropriately. Here we propose novel MU methods based on stochastic neighbor relationship, by extending dimensionality reduction methods, Stochastic Neighbor Embed- ding (SNE) and t-distributed SNE. The proposed methods are defined by Kullback-Leibler divergence (KL divergence), and because of the asymmetric property of KL divergence, they give priority to representing relationships between relevant pairs. Experimental results show that the proposed methods can alleviate the problem and achieve reasonable visualization compared to the conventional MU.