Hierarchical Neighbors Embedding.

Abstract

Manifold learning now plays an important role in machine learning and many relevant applications. In spite of the superior performance of manifold learning techniques in dealing with nonlinear data distribution, their performance would drop when facing the problem of data sparsity. It is hard to obtain satisfactory embeddings when sparsely sampled high-dimensional data are mapped into the observation space. To address this issue, in this article, we propose hierarchical neighbors embedding (HNE), which enhances the local connections through hierarchical combination of neighbors. And three different HNE-based implementations are derived by further analyzing the topological connection and reconstruction performance. The experimental results on both the synthetic and real-world datasets illustrate that our HNE-based methods could obtain more faithful embeddings with better topological and geometrical properties. From the view of embedding quality, HNE develops the outstanding advantages in dealing with data of general distributions. Furthermore, comparing with other state-of-the-art manifold learning methods, HNE shows its superiority in dealing with sparsely sampled data and weak-connected manifolds.