Tangent space guided intelligent neighbor finding

We present an intelligent neighbor-finding algorithm called SAFFRON that chooses neighboring points while avoiding making connections between points on geodesically distant regions of a manifold. SAFFRON identifies the suitability of points to be neighbors by using a relaxation technique that alternately estimates the tangent space at each point, and measures how well the estimated tangent spaces align with each other. This technique enables SAFFRON to form high-quality local neighborhoods, even on manifolds that pass very close to themselves. SAFFRON is even able to find neighborhoods that correctly follow the manifold topology of certain self-intersecting manifolds.