Parameterless Isomap with Adaptive Neighborhood Selection

Isomap is a highly popular manifold learning and dimensionality reduction technique that effectively performs multidimensional scaling on estimates of geodesic distances. However, the resulting output is extremely sensitive to parameters that control the selection of neighbors at each point. To date, no principled way of setting these parameters has been proposed, and in practice they are often tuned ad hoc, sometimes empirically based on prior knowledge of the desired output. In this paper we propose a parameterless technique that adaptively defines the neighborhood at each input point based on intrinsic dimensionality and local tangent orientation. In addition to eliminating the guesswork associated with parameter configuration, the adaptive nature of this technique enables it to select optimal neighborhoods locally at each point, resulting in superior performance.