Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Joint matrix triangularization is often used for estimating the joint eigenstructure of a set M of matrices, with applications in signal processing and machine learning.  consider the problem of approximate joint matrix triangularization when the matrices in M are jointly diagonalizable and real, but  only observe a set M' of noise perturbed versions of the matrices in M. Our main result is a first-order upper bound on the distance beten any approximate joint triangularizer of the matrices in M' and any exact joint triangularizer of the matrices in M. The bound depends only on the observable matrices in M' and the noise level. In particular, it does not depend on optimization specific properties of the triangularizer, such as its proximity to critical points, that are typical of existing bounds in the literature. To our knowledge, this is the first a posteriori bound for joint matrix decomposition.  demonstrate the bound on synthetic data for which the ground truth is known.
['Nicolo Colombo', 'Nikos A. Vlassis']
I am writing a research paper on a idea A posteriori error bounds for joint matrix decomposition problems
[{"from": "human", "value": "I am writing a research paper on a idea A posteriori error bounds for joint matrix decomposition problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Joint matrix triangularization is often used for estimating the joint eigenstructure of a set M of matrices, with applications in signal processing and machine learning.  consider the problem of approximate joint matrix triangularization when the matrices in M are jointly diagonalizable and real, but  only observe a set M' of noise perturbed versions of the matrices in M. Our main result is a first-order upper bound on the distance beten any approximate joint triangularizer of the matrices in M' and any exact joint triangularizer of the matrices in M. The bound depends only on the observable matrices in M' and the noise level. In particular, it does not depend on optimization specific properties of the triangularizer, such as its proximity to critical points, that are typical of existing bounds in the literature. To our knowledge, this is the first a posteriori bound for joint matrix decomposition.  demonstrate the bound on synthetic data for which the ground truth is known."}]