Distance Preserving Embeddings for General n-Dimensional Manifolds

作者：Verma Nakul^*

来源：Journal of Machine Learning Research, 2013, 14: 2415-2448.

• manifold learning
• isometric embeddings
• non-linear dimensionality reduction
• Nash's embedding theorem

Low dimensional embeddings of manifold data have gained popularity in the last decade. However, a systematic finite sample analysis of manifold embedding algorithms largely eludes researchers. Here we present two algorithms that embed a general n-dimensional manifold into R-d (where d only depends on some key manifold properties such as its intrinsic dimension, volume and curvature) that guarantee to approximately preserve all interpoint geodesic distances.

• 出版日期2013-8