A new method of selecting safe neighbors for the Riemannian Manifold Learning algorithm

Manifold learning (ML) comprehends a set of nonlinear techniques for mining and representing high-dimensional data. In this work, we approach the well-known and successful ML technique called Riemannian Manifold Learning (RML). Firstly, we present a geometric interpretation of the main steps of selecting visible and safe neighborhoods to reconstruct geometry and topology in the original RML algorithm. Then, we describe and implement a new method of selecting safe neighbors for this algorithm. Our experimental results on synthetic and real data sets, using open source tools and a public face image database, have showed that the new method proposed shows similar results to the original one and reconstructions that favour local rather than holistic similarities described by the data. Additionally, since the new method proposed requires the specification of only one input parameter, its implementation is simpler and more intuitive than the original one.