Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Low dimensional embeddings of manifold data have gained popularity in the last decade. Hover, a systematic finite sample analysis of manifold embedding algorithms largely eludes researchers. Here  present two algorithms that embed a general n-dimensionalmanifold into Rd (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.
['Nakul Verma']
I am writing a research paper on a idea Distance preserving embeddings for general n-dimensional manifolds
[{"from": "human", "value": "I am writing a research paper on a idea Distance preserving embeddings for general n-dimensional manifolds"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Low dimensional embeddings of manifold data have gained popularity in the last decade. Hover, a systematic finite sample analysis of manifold embedding algorithms largely eludes researchers. Here  present two algorithms that embed a general n-dimensionalmanifold into Rd (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."}]