Analysing hyperbolic representations for use in recommendations in social networks

Abstract

Recommender systems play an important role in helping online users find relevant information by suggesting content that can be of potential interest to them. Different Social networks have indicated hierarchical structures in the past. Recently, hyperbolic representations have been developed to model latent hierarchical structures. Hyperbolic Hierarchical Clustering(HypHC) is one such technique. We propose using HypHC representations as a dimensionality reduction step for recommendations in social networks made using nearest neighbour based algorithms. Using HypHC should result in two main advantages over embeddings in euclidean space. First, it can effectively capture tree structures. Second, it is capable of modeling complex data in lower dimensionsal space because the hyperbolic space expands exponentially with radius, while the euclidean space grows only polynomially. For our experiment, we represent the features of users on Reddit in the hyperbolic space in 2 dimensions using HypHC. On comparing the quality of the clustering tree obtained by HypHC to different similairity based hierarchical clustering methods, it was found out that HypHC gave the lowest discrete dasgupta cost. We compared the HypHC embeddings with PCA embeddings as a dimensionality reduction step for two nearest neighbour approaches for subreddit recommendation. It was found that recommendations using HypHC performed similarly to recommendations using PCA. In fact, the hyperbolic embeddings even outperformed PCA slightly for one of the approaches.