Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Graph matching is an important problem in machine learning and pattern recognition. Herein,  present theoretical and practical results on the consistency of graph matching for estimating a latent alignment function beten the vertex sets of two graphs, as ll as subsequent algorithmic implications when the latent alignment is partially observed. In the correlated Erdos-Renyi graph setting,  prove that graph matching provides a strongly consistent estimate of the latent alignment in the presence of even modest correlation.  then investigate a tractable, restricted-focus version of graph matching, which is only concerned with adjacency involving vertices in a partial observation of the latent alignment;  prove that a logarithmic number of vertices whose alignment is known is sufficient for this restricted-focus version of graph matching to yield a strongly consistent estimate of the latent alignment of the remaining vertices.  show how Frank-Wolfe methodology for approximate graph matching, when there is a partially observed latent alignment, inherently incorporates this restricted-focus graph matching. Lastly,  illustrate the relationship beten seeded graph matching and restricted-focus graph matching by means of an illuminating example from human connectomics.
['Vince Lyzinski', 'Donniell E. Fishkind', 'Carey E. Priebe']
I am writing a research paper on a idea Seeded graph matching for correlated Erdös-Rényi graphs
[{"from": "human", "value": "I am writing a research paper on a idea Seeded graph matching for correlated Erd\u00f6s-R\u00e9nyi graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Graph matching is an important problem in machine learning and pattern recognition. Herein,  present theoretical and practical results on the consistency of graph matching for estimating a latent alignment function beten the vertex sets of two graphs, as ll as subsequent algorithmic implications when the latent alignment is partially observed. In the correlated Erdos-Renyi graph setting,  prove that graph matching provides a strongly consistent estimate of the latent alignment in the presence of even modest correlation.  then investigate a tractable, restricted-focus version of graph matching, which is only concerned with adjacency involving vertices in a partial observation of the latent alignment;  prove that a logarithmic number of vertices whose alignment is known is sufficient for this restricted-focus version of graph matching to yield a strongly consistent estimate of the latent alignment of the remaining vertices.  show how Frank-Wolfe methodology for approximate graph matching, when there is a partially observed latent alignment, inherently incorporates this restricted-focus graph matching. Lastly,  illustrate the relationship beten seeded graph matching and restricted-focus graph matching by means of an illuminating example from human connectomics."}]