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

Abstract

Manifold learning comprehends a set of non-linear techniques for mining and representing high-dimensional data. In this work, we firstly present a geometric interpretation of the main steps of selecting visible and safe neighborhoods to reconstruct geometry and topology in the Riemannian Manifold Learning 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 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.