Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   show that many kernel methods can be adapted to deal with indefinite kernels, that is, kernels which are not positive semidefinite. They do not satisfy Mercer's condition and they induce associated functional spaces called Reproducing Kernel Kreǐn Spaces (RKKS), a generalization of Reproducing Kernel Hilbert Spaces (RKHS).Machine learning in RKKS shares many "nice" properties of learning in RKHS, such as orthogonality and projection. Hover, since the kernels are indefinite,  can no longer minimize the loss, instead  stabilize it.  show a general representer theorem for constrained stabilization and prove generalization bounds by computing the Rademacher averages of the kernel class.  list several examples of indefinite kernels and investigate regularization methods to solve spline interpolation. Some preliminary experiments with indefinite kernels for spline smoothing are reported for truncated spectral factorization, Landber-Fridman iterations, and MR-II.
['Cheng Soon Ong', 'Xavier Mary', 'Stéphane Canu', 'Alexander J. Smola']
I am writing a research paper on a idea Learning with non-positive kernels
[{"from": "human", "value": "I am writing a research paper on a idea Learning with non-positive kernels"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   show that many kernel methods can be adapted to deal with indefinite kernels, that is, kernels which are not positive semidefinite. They do not satisfy Mercer's condition and they induce associated functional spaces called Reproducing Kernel Kre\u01d0n Spaces (RKKS), a generalization of Reproducing Kernel Hilbert Spaces (RKHS).Machine learning in RKKS shares many \"nice\" properties of learning in RKHS, such as orthogonality and projection. Hover, since the kernels are indefinite,  can no longer minimize the loss, instead  stabilize it.  show a general representer theorem for constrained stabilization and prove generalization bounds by computing the Rademacher averages of the kernel class.  list several examples of indefinite kernels and investigate regularization methods to solve spline interpolation. Some preliminary experiments with indefinite kernels for spline smoothing are reported for truncated spectral factorization, Landber-Fridman iterations, and MR-II."}]