Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In a typical linear data compression system the representation variables resulting from the coding operation are assumed totally reliable and therefore the solution in the mean-squared-error sense is an orthogonal projector to the so-called principal component subspace. When the representation variables are contaminated by additive noise which is uncorrelated with the signal, the problem is called noisy principal component analysis (NPCA) and the optimal MSE solution is not a trivial extension of PCA.  show that: the problem is not ll defined unless  impose explicit or implicit constraints on either the coding or the decoding operator; orthogonality is not a property of the optimal solution under most constraints; and the signal components may or may not be reconstructed depending on the noise level. As the noise por increases,  observe rank reduction in the optimal solution under most reasonable constraints. In these cases it appears that it is preferable to omit the smaller signal components rather than attempting to reconstruct them. Finally,  show that standard Hebbian-type PCA learning algorithms are not optimally robust to noise, and propose a new Hebbian-type learning algorithm which is optimally robust in the NPCA sense.
['Konstantinos I. Diamantaras', 'Kurt Hornik', 'Michael G. Strintzis']
I am writing a research paper on a idea Optimal linear compression under unreliable representation and robust PCA neural models
[{"from": "human", "value": "I am writing a research paper on a idea Optimal linear compression under unreliable representation and robust PCA neural models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In a typical linear data compression system the representation variables resulting from the coding operation are assumed totally reliable and therefore the solution in the mean-squared-error sense is an orthogonal projector to the so-called principal component subspace. When the representation variables are contaminated by additive noise which is uncorrelated with the signal, the problem is called noisy principal component analysis (NPCA) and the optimal MSE solution is not a trivial extension of PCA.  show that: the problem is not ll defined unless  impose explicit or implicit constraints on either the coding or the decoding operator; orthogonality is not a property of the optimal solution under most constraints; and the signal components may or may not be reconstructed depending on the noise level. As the noise por increases,  observe rank reduction in the optimal solution under most reasonable constraints. In these cases it appears that it is preferable to omit the smaller signal components rather than attempting to reconstruct them. Finally,  show that standard Hebbian-type PCA learning algorithms are not optimally robust to noise, and propose a new Hebbian-type learning algorithm which is optimally robust in the NPCA sense."}]