大规模分布式矩阵分解算法的理论与应用研究

Matrix factorization is of great important in many fields such as artificial intelligence, statistics, machine learning, and data mining. In recent years, with the rapid development of internet technologies, the volume of data has been increasing exponentially, which poses huge challenges on matrix factorization computations. It is now common to do data-intensive computations on massive distributed platforms, which has been proved very successful. However, research on distributed matrix factorization is still quite limited. For the lack of general algorithmic frameworks and techniques, this project proposes a divide-and-conquer framework based on theories of nonlinear optimization and numerical iterative methods. To further reduce the communication burden, this project will apply novel distributed matrix compression and round compression techniques. To theoretically analyze these algorithms, the project will propose a rigorous and clean computation model. Finally, all algorithms designed will be integrated into Spark. The success of the project will potentially make matrix factorization computation much more scalable, which will support the development of large scale applications such as recommendation systems. Moreover, the new ideas and techniques proposed in this project will be likely to advance the research of data-intensive distributed computation.

矩阵分解在人工智能，统计学，机器学习和数据挖掘中有着极为重要的科学和应用价值。近些年，随着互联网的快速发展，数据的规模呈指数级上涨，这给矩阵分解计算提出来极大的挑战。目前，大规模分布式计算已经成为解决数据密集型问题最常用、最有效方法。然而，分布式矩阵分解算法目前还没有得到很好的研究。针对现有研究缺乏通用算法框架和算法技术的不足，该项目拟提出以非线性优化和数值迭代方法为理论基础的分治算法设计框架。为了进一步降低分布式算法中的通信代价，本项目拟采用新的分布式矩阵压缩和通信轮次压缩技术。为了从理论上分析所提算法的复杂性和计算精度，该课题拟提出严谨、简洁且符合实际的理论分析模型。最终将所提算法集成到分布式计算平台Spark上。该项目的完成有望大大提高矩阵分解计算的可扩展性，为推荐系统等大规模应用提供技术支撑。同时，该项目中提出的新思路和新技术对与促进数据密集型分布式计算领域的发展也具有重要意义。

矩阵分解在人工智能，统计学，机器学习和数据挖掘中有着极为重要的科学和应用价值。近些年，随着互联网的快速发展，数据的规模呈指数级上涨，这给矩阵分解计算提出来极大的挑战。目前，大规模分布式计算已经成为解决数据密集型问题最常用、最有效方法。然而，分布式矩阵分解算法目前还没有得到很好的研究。针对现有研究缺乏通用算法框架和算法技术的不足，该项目提出以非线性优化和数值迭代方法为理论基础的分治算法设计框架。为了进一步降低分布式算法中的通信代价，本项目采用新的分布式矩阵压缩技术和分布式梯度采样和量化算法。本课题从理论上分析所提算法的复杂性和计算精度。该项目所提算法，有望大大提高工业场景下矩阵分解计算的可扩展性，为推荐系统等大规模应用提供技术支撑。同时，该项目中提出的新思路和新技术对与促进数据密集型分布式计算领域的发展也具有一定指导意义。