Speaker:    

吴钢 教授，中国矿业大学数学学院
Inviter:      
Title:
    New Algorithms for Trace-Ratio Problem with Application to High-Dimension and Large-Sample Data Dimensionality Reduction
Time & Venue:
    2021.09.11 10:00-11:00 腾讯会议ID：830 860 639
Abstract:
    

摘要详见附件

Abstract：
Learning  large-scale  data  sets  with  high  dimensionality  is  a  main concern in research areas including machine learning, visual recognition,  information  retrieval,  to  name  a  few.  In  many  practical uses such as images, video, audio, and text processing, we have to face with high-dimension and large-sample data problems. The trace-ratio  problem  is  a  key  problem  for  feature  extraction  and dimensionality  reduction  to  circumvent  the  high  dimensional  space. However, it has been long believed that this problem has no closed-form solution, and one has to solve it by using some inner-outer iterative algorithms that are very time-consuming. Therefore,  efficient  algorithms  for  high-dimension  and  large-sample trace-ratio problems are still lacking, especially for dense data problems.  In  this  work,  we  present  a  closed-form  solution  for  the trace-ratio problem, and propose two algorithms to solve it. Based on the  formula  and  the  randomized  singular  value  decomposition,  we first propose a randomized algorithm for solving high-dimension and large-sample  dense  trace-ratio  problems.  For  high-dimension  and large-sample sparse trace-ratio problems, we then propose an algorithm based on the closed-form solution and solving some consistent  under-determined  linear  systems.  Theoretical  results  are established  to  show  the  rationality  and  efficiency  of  the  proposed methods.  Numerical  experiments  are  performed  on  some  real-world data sets, which illustrate the superiority of the proposed algorithms over many state-of-the-art algorithms for high-dimension and large-sample dimensionality reduction problems.
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