Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Multidimensional-scaling (MDS) is an information analysis tool. It involves the evaluation of distances beten data points, which is a quadratic space-time problem. Then, MDS procedures find an embedding of the points in a low dimensional Euclidean (flat) domain, optimizing for the similarity of inter-points distances.  present an efficient solver for Classical Scaling (a specific MDS model) by extending the distances measured from a subset of the points to the rest, while exploiting the smoothness property of the distance functions. The smoothness is measured by the L2 norm of the Laplace-Beltrami operator applied to the unknown distance function. The Laplace Beltrami reflects the local differential relations beten points, and can be computed in linear time. Classical-scaling is thereby reformulated into a quasi-linear space-time complexities procedure.
['Gil Shamai', 'Yonathan Aflalo', 'Michael Zibulevsky', 'Ron Kimmel']
I am writing a research paper on a idea Classical Scaling Revisited
[{"from": "human", "value": "I am writing a research paper on a idea Classical Scaling Revisited"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Multidimensional-scaling (MDS) is an information analysis tool. It involves the evaluation of distances beten data points, which is a quadratic space-time problem. Then, MDS procedures find an embedding of the points in a low dimensional Euclidean (flat) domain, optimizing for the similarity of inter-points distances.  present an efficient solver for Classical Scaling (a specific MDS model) by extending the distances measured from a subset of the points to the rest, while exploiting the smoothness property of the distance functions. The smoothness is measured by the L2 norm of the Laplace-Beltrami operator applied to the unknown distance function. The Laplace Beltrami reflects the local differential relations beten points, and can be computed in linear time. Classical-scaling is thereby reformulated into a quasi-linear space-time complexities procedure."}]