Nonlinear Dimension Reduction Method Of Component Data Based On Diffusion Kernel

With the improvement of computer’s ability to store and process data,high-dimension data is becoming more and more popular in many disciplines.The demand for effective methods to extract useful information from these data inevitably leads to dimension reduction,which has experienced great development in the past 20 years.Component data is a kind of special data,which satisfies the condition of definite sum.It exists in many fields and is widely used.Under the constraint of definite sum of component data,the algorithm of Euclid space is not applicable.Simplex vector space provides a set of complete and simple rules for component data.Because the component data has the characteristics of definite sum,the linear dimension reduction is not suitable for the component data,and the nonlinear dimension reduction method should be used.Among the nonlinear dimension reduction methods,the kernel method is the most important.However,because the component data is defined in simplex space,some common kernels are not applicable,because the distances represented by these kernels are defined in Euclid space.In this paper,the diffusion kernel on the manifold is introduced into the method of nonlinear dimension reduction.The idea is that the diffusion kernel is the kernel defined on the manifold,and the effect may be better than the kernels defined on Euclid space.In this paper,this view is proved by numerical results.