低秩距离学习及其应用

项目名称： 低秩距离学习及其应用

项目编号： No.61272247

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： 卢宏涛

作者单位： 上海交通大学

项目金额： 81万元

中文摘要： 近年来，数据点之间的距离/度量学习已成为模式识别和机器学习领域的一个研究热点。现有的距离/度量学习方法主要是利用数据点之间的成对约束关系来学习数据点之间的一个良好的距离度量，即距离参数矩阵，没有考虑低秩性。实际问题中的数据通常具有低秩特征，即数据点之间相互依存。本项目在数据点之间的距离/度量学习的过程中考虑这种低秩特性，开展低秩距离学习的研究。针对数据低秩的特性，研究新的低秩距离学习框架，提出基于矩阵核范数最小化的低秩距离学习模型，并将保结构学习特性引入到距离学习中，使得经过距离变换的数据点在新的空间具有保结构的性质，进一步扩展低秩距离学习理论；研究低秩距离学习优化问题的快速求解算法，提出基于近似梯度、奇异值阈值化及交替方向的快速算法；将提出的低秩距离学习方法应用于基于内容的图像检索、图像分类识别以及成对约束传递问题中。力争在低秩距离学习理论、算法和应用方面取得创新性成果。

中文关键词： 矩阵分解；哈希；距离学习；成对约束；低秩

英文摘要： Recently, the distance/metric learning between data points has become a hot research topic in the area of pattern recognition and machine learning. The current methods to this problem aim to learn a better distance metric, i.e. the distance parameter matrix, between data points by using the pair-wise constraints, but have not taken the low rank into consideration. In reality, there exists the low-rank property between data points, i.e., the data points depend on each other. In this project, we wish to consider such low-rank property in the process of the distance/metric learning and carry out the research of low-rank distance learning. According to the low-rank property of the data, we will investigate the new low-rank distance/metric learning framework, propose new low-rank distance learning models based on matrix nuclear norm minimization, and we will also introduce the locality preserving learning into the low-rank distance learning to ensure the transformed data to have the property to preserve the locality property, so as to further extend the low-rank distance learning model; we will propose a set of faster solving algorithms for the low-rank distance learning model, based on the proximal gradient method, the singular value thresholding method and the alternating direction method. we will apply the propose

英文关键词： Matrix factorization；Hashing；Distance learning；pairwise constrains；Low-rank