Sparse Radial Basis Function Neural Network And Its Applications

The main research content of this paper is the sparse radial basis function neural net-work structure and its algorithm implementation.And we apply it to the problems of image representation and Gaussian molecular surface representation.Based on this,this paper conducts research on sparse radial basis function neural net-work and its applications,mainly divided into two parts:image representation based on sparse ellipse RBF Neural Network,and Gaussian molecular surface representation based on sparse ellipsoid RBF Neural Network as follows:(1)Image representation based on sparse ellipse RBF Neural Network.In this part,we propose a sparse representation model of image data,that is,a sparse ellipse RBF Neu-ral Network model.We can use the model to approximate the input image and achieve the sparsity of the image representation by solving a nonlinear optimization problem with L1 regularization.For complicated image data,if we use a general Gaussian function as the activation function of the hidden layer of the network,there are some limitations to approx-imation for RBF Neural Network,which will cause the model to require a large number of basis functions while approximating the input surface.In this regard,we construct a general ellipse Gaussian function based on the geometric characteristics of the principal axis in any direction,and select it as the activation function of the hidden layer.The experimental results demonstrate that the input image can be represented with relative higher accuracy by fewer ellipse Gaussian functions.(2)Gaussian molecular surface representation based on sparse ellipsoid RBF Neural Network.In this part,we propose a sparse representation model of the Gaussian molecular surface,namely a sparse ellipsoid RBF Neural Network model.Similarly,for complicated geometric shapes,the approximation of general RBF Neural Network has certain limitations.The method of the rotation mechanism for the ellipsoid feature is introduced to construct a general ellipsoid Gaussian function for expanding the approximation ability of RBF Neural Network.It is selected as the activation function of the hidden layer.Based on the sparse optimization framework,we can approximate the input Gaussian molecular surface using an ellipsoid RBF Neural Network.The experimental results show that our method can accurate-ly represent the input Gaussian molecular surface through a set of sparser ellipsoid Gaussian functions.