实值多变量维数约简研究及应用

项目名称： 实值多变量维数约简研究及应用

项目编号： No.61273299

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 张军平

作者单位： 复旦大学

项目金额： 76万元

中文摘要： 维数约简在处理维数灾问题、帮助加速算法的计算效率和提高可解释性以及数据可视化起着至关重要的作用。常见的维数约简方法较少考虑响应变量与高维数据集间的联系，因而获得的约简空间在预测未知响应变量时性能不是最优的。要基于高维数据集预测未知响应变量，更一般和合理的办法是在约简的同时考虑响应变量是光滑变化的情况，即研究响应变量属于实值多变量域(real-valued multivariate domain)时的维数约简。本项目将针对现有实值多变量维数约简研究的不足，研究以下五个方向：1）保持拓扑结构的实值多变量维数约简方法研究；2）基于非线性嵌入的实值多变量维数约简方法研究；3）基于实值多变量维数约简的数据空间划分；4)时序数据的实值多变量维数约简方法研究；5）基于概率图模型的实值多变量维数约简研究。本项目也将基于以上的研究成果选择生物认证和智能交通领域的一至两个方向展开应用性基础研究。

中文关键词： 维数约简；实值多变量；半监督学习；随机分布特征；深度学习

英文摘要： Dimension Reduction plays an important role in addressing "curse of dimensionaity" issue, speeding up the computational efficiency of algorithms, enhancing the interpretation to data as well as data visualization. The conventional dimension reduction methods pay less attention to the relationship betwwen high-dimensioal data and response variables. Therefore, the performance of predicting unseen repsonse variables based on such a reduction may not be optimal. To predict the unseen response variables given a high-dimensional dataset, one general and reasonable way is to reduce the dimension of data under the condition that response variables are smoothly changed. That is to say, to investigate real-valued multivariate dimension reduction. In this project, we will consider the pros and cons of current researches in real-valued multivariate dimension reduction, and investigate the following five directions: 1) topological preserved real-valued multivariate dimension reduction; 2) nonlinear embedding-based real-valued multivariate dimension reduction; 3) real-valued multivariate dimension reduction-based data space partitioning; 4) temporal real-valued multivariate dimension reduction; 5) probablistic graph model-based real-valued multivariate dimension reduction. We will select one or more directions in biometric

英文关键词： Dimension reduction；Real-value multi-variables；Semi-supervised learning；Random distribution features；Deep learning