Colloquiums and Conferences

Three Experts From Sun Yat-sen University reported their work in School of Mathematical Science

Time: 2018-10-12 19:01:00

Multi-task Learning in Vector-valued Reproducing Kernel Banach Spaces with the L1 Norm.

Speaker：Researcher Rongrong Lin Sun Yat-sen University(SYSU)

Time：2018-10-12 09:00--10:00

Location：Room 401 in School of Mathematical Sciences

Introduction：

Motivated by sparse multi-task learning, we constructed a class of vector-valued reproducing kernel Banach spaces with the l1 norm based on multi-task admissible kernels. The linear representer theorem holds for regularization networks in the obtained spaces if and only if the Lebesgue constant of multi-task admissible kernels is bounded by 1. Examples including the Brownian bridge kernel, the exponential kernel and the covariance of Brownian motion admissible for constructions are given. In order to accommodate more kernels, we consider relaxed representer theorems that need a weaker condition on the Lebesgue constant. Finally, we present numerical experiments for both synthetic data and real-world benchmark data to demonstrate the advantages of the proposed construction and regularization models. This is a joint work with Prof.Guohui Song (Clarkson University) and Haizhang Zhang (SYSU).

微信图片_20181016000013_副本.jpg

A Higher-Order Polynomial Method for SPECT Reconstruction

Speaker：Professor Si Li Sun Yat-sen University(SYSU)

Time：2018-10-12 10:00--11:00

Location：Room 401 in School of Mathematical Sciences

Introduction：

Existing single-photon emission computed tomography (SPECT) reconstruction methods are most based on discrete models that may be viewed as piecewise constant approximations of certain continuous data acquisition process. Due to low accuracy order of piecewise constant approximations, traditional discrete models introduce irreducible model errors which are a bottleneck of the quality improvement of reconstructed images in clinical applications. To overcome this drawback, we develop a higher-order polynomial method for SPECT reconstruction. Specifically, we represent the data acquisition of SPECT imaging by using an integral equation model, approximate the solution of the underlying integral equation by higher-order piecewise polynomials leading to a new discrete system and introduce two novel regularizers for the system, by exploring the a priori knowledge of the radiotracer distribution, suitable for the approximation.

微信图片_20181015235135_副本.jpg

High Dimension Sparse Grid Approximation Techniques and its Application in Integral Equation and Random Differential Equation

Speaker：Professor Ying Jiang Sun Yat-sen University(SYSU)

Time：2018-10-12 11:00--12:00

Location：Room 401 in School of Mathematical Sciences

Introduction：

This talk is about a kind of high-dimension approximation techniques, called sparse grids,which are widely used in solving partial differential equations, integral equations,designing high-dimension quadrature formula, data mining, etc. The approximation schemes on sparse grids achieve quasi-linear computational cost when the schemes on full grids suffer from the ``curse of dimensionality'', since the computational complexity increases exponentially as the dimension grows. At same time, the approximation schemes on sparse grids enjoy the optimal approximation order as the schemes on full grids do.

微信图片_20181015235708_副本.jpg

微信图片_20181015234720_副本.jpg