Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  reconsider randomized algorithms for the low-rank approximation of SPSD matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results consist of an empirical evaluation of the performance quality and running time of sampling and projection methods on a diverse suite of SPSD matrices. Our results highlight complementary aspects of sampling versus projection methods, and they point to dierences beten uniform and nonuniform sampling methods based on leverage scores.  complement our empirical results with a suite of worst-case theoretical bounds for both random sampling and random projection methods. These bounds are qualitatively superior to existing bounds|e.g., improved additive-error bounds for spectral and Frobenius norm error and relative-error bounds for trace norm error.
['Alex Gittens', 'Michael W. Mahoney']
I am writing a research paper on a idea Revisiting the Nystrom method for improved large-scale machine learning
[{"from": "human", "value": "I am writing a research paper on a idea Revisiting the Nystrom method for improved large-scale machine learning"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  reconsider randomized algorithms for the low-rank approximation of SPSD matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results consist of an empirical evaluation of the performance quality and running time of sampling and projection methods on a diverse suite of SPSD matrices. Our results highlight complementary aspects of sampling versus projection methods, and they point to dierences beten uniform and nonuniform sampling methods based on leverage scores.  complement our empirical results with a suite of worst-case theoretical bounds for both random sampling and random projection methods. These bounds are qualitatively superior to existing bounds|e.g., improved additive-error bounds for spectral and Frobenius norm error and relative-error bounds for trace norm error."}]