Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  focus on the problem of finding a non-linear classification function that lies in a Reproducing Kernel Hilbert Space (RKHS) both from the primal point of view (finding a perfect separator when one exists) and the dual point of view (giving a certificate of non-existence), with special focus on generalizations of two classical schemes - the Perceptron (primal) and Von-Neumann (dual) algorithms.#R##N##R##N# cast our problem as one of maximizing the regularized normalized hard-margin (ρ) in an RKHS and rephrase it in terms of a Mahalanobis dot-product/semi-norm associated with the kernel's (normalized and signed) Gram matrix.  derive an accelerated smoothed algorithm with a convergence rate of √log n/ρ given n separable points, which is strikingly similar to the classical kernelized Perceptron algorithm whose rate is 1/ρ2. When no such classifier exists,  prove a version of Gordan's separation theorem for RKHSs, and give a reinterpretation of negative margins. This allows us to give guarantees for a primal-dual algorithm that halts in min{√n/|ρ|,√n/e} iterations with a perfect separator in the RKHS if the primal is feasible or a dual e-certificate of near-infeasibility.
['Aaditya Ramdas', 'Javier Pe?a']
I am writing a research paper on a idea Margins, Kernels and Non-linear Smoothed Perceptrons
[{"from": "human", "value": "I am writing a research paper on a idea Margins, Kernels and Non-linear Smoothed Perceptrons"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  focus on the problem of finding a non-linear classification function that lies in a Reproducing Kernel Hilbert Space (RKHS) both from the primal point of view (finding a perfect separator when one exists) and the dual point of view (giving a certificate of non-existence), with special focus on generalizations of two classical schemes - the Perceptron (primal) and Von-Neumann (dual) algorithms.#R##N##R##N# cast our problem as one of maximizing the regularized normalized hard-margin (\u03c1) in an RKHS and rephrase it in terms of a Mahalanobis dot-product/semi-norm associated with the kernel's (normalized and signed) Gram matrix.  derive an accelerated smoothed algorithm with a convergence rate of \u221alog n/\u03c1 given n separable points, which is strikingly similar to the classical kernelized Perceptron algorithm whose rate is 1/\u03c12. When no such classifier exists,  prove a version of Gordan's separation theorem for RKHSs, and give a reinterpretation of negative margins. This allows us to give guarantees for a primal-dual algorithm that halts in min{\u221an/|\u03c1|,\u221an/e} iterations with a perfect separator in the RKHS if the primal is feasible or a dual e-certificate of near-infeasibility."}]