稀疏优化问题的理论与方法及其应用

项目名称： 稀疏优化问题的理论与方法及其应用

项目编号： No.11471159

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 王丽平

作者单位： 南京航空航天大学

项目金额： 62万元

中文摘要： 本项目将提供稀疏优化问题的理论分析和算法设计，从向量、矩阵两种角度建立模型，并将之应用于高维数据的模式识别。主要内容有：1)针对生物基因表达数据高维数、低采样的特点，引入稀疏优化模型表示基因间的交互关系，结合统计两分类t-test和独立法则，确定出优化和统计意义下最具识别能力的基因。2)为适应不同的稀疏结构，建立广义的混合l2,p(0

中文关键词： 非线性规划；最优化理论与方法；数值优化；信赖域方法；数据挖掘

英文摘要： This proposal presents the theory analysis and algorithm design of sparse optimization. Form the views of vector and matrix, a variety of sparse models will be constructed and applied to pattern recognition for high dimensional data. It mainly contains: 1) According to the biological features of gene expression data, higher dimension but lower sampling, a special sparse optimization is introduced to represent the inter-relation between genes. Under two classes independence rule, the most discriminative features are determined in the optimal and statistical senses. 2) A generalized l2,p(0<p<=1)-norm minimizations will be considered and a unified algorithm is proposed, also the involved convergence. The results provide algorithmic support to adaptively choose better sparse model for different sparse data structures. 3) Based on the theoretical results about l1-mimization problems, also considering the matrix norm nature, this proposal will discuss the joint sparsity, computational complexity and robustness of non-convex and non-Lipschitz continuous l2,p(1<p<=1) based minimization problem.4) To overcome the inefficiency of determining goals one by one, a joint sparse model is constructed with different distrbution pattern. Based on the conclusions in 2) and 3), a unified algorithm and its convergence analysis will be presented. The new algorithm will be also applied to robust face recognition.

英文关键词： Nonlinear Programming;Theory and Methods of Optimization;Numerical Optimization;Trust Region Methods;Data Mining