Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Complex objects can often be conveniently represented by finite sets of simpler components, such as images by sets of patches or texts by bags of words.  study the class of positive definite (p.d.) kernels for two such objects that can be expressed as a function of the merger of their respective sets of components.  prove a general integral representation of such kernels and present two particular examples. One of them leads to a kernel for sets of points living in a space endod itself with a positive definite kernel.  provide experimental results on a benchmark experiment of handwritten digits image classification which illustrate the validity of the approach.
['Marco Cuturi', 'Jean-Philippe Vert']
I am writing a research paper on a idea Semigroup Kernels on Finite Sets
[{"from": "human", "value": "I am writing a research paper on a idea Semigroup Kernels on Finite Sets"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Complex objects can often be conveniently represented by finite sets of simpler components, such as images by sets of patches or texts by bags of words.  study the class of positive definite (p.d.) kernels for two such objects that can be expressed as a function of the merger of their respective sets of components.  prove a general integral representation of such kernels and present two particular examples. One of them leads to a kernel for sets of points living in a space endod itself with a positive definite kernel.  provide experimental results on a benchmark experiment of handwritten digits image classification which illustrate the validity of the approach."}]