Dimensinality Reduction in BIG DATA ERA
1.Dimensinality Reduction in BIG DATA ERA
2. A Randomized GLRAM algorithm for high dimensionality reduction and image reconstruction
High-dimensionality reduction techniques are very important tools in machine learning and data mining. The method of generalized low rank approximations of matrices (GLRAM) is a popular technique for dimensionality reduction and image reconstruction. However, it suffers from heavily computational overhead in practice, especially for data with high dimensionality. In order to reduce the computational complexities of this algorithm, we first propose a randomized GLRAM algorithm based on randomized singular value decomposition (RSVD). The theoretical contribution of our work is three-fold.
First, we discuss the decaying property of singular values of the matrices during iterations of the GLRAM algorithm, and provide a target rank required in the RSVD process from a theoretical point of view. Second, we establish the relationship between the reconstruction errors generated by the original GLRAM algorithm and the randomized GLRAM algorithm. It is shown that the reconstruction errors generated by the GLRAM algorithm and the proposed randomized GLRAM algorithm are comparable, even if the solutions are computed inaccurately during iterations.
Third, the convergence of the randomized GLRAM algorithm is considered. Numerical experiments on some real-world data sets illustrate the superiority of our proposed algorithm over its original counterpart and some state-of-the-art GLRAM-type algorithms.
Numerical experiments on some real-world data sets illustrate the superiority of our proposed algorithm over its original counterpart and some state-of-the-art GLRAM-type algorithms.
报 告 人：
吴钢 教授 （ 中国矿业大学）
Tencent会议号： 560 132 762
报告人概况：吴钢，博士、中国矿业大学数学学科教授、博士生导师，江苏省“333工程”中青年科学技术带头人，江苏省“青蓝工程”中青年学术带头人，现任江苏省计算数学学会副理事长。主要研究方向：大规模科学与工程计算、数据挖掘与机器学习、大数据相关快速算法等。先后主持国家自然科学基金、江苏省省自然科学基金项目多项，在国际知名杂志，如：SIAM Journal on Numerical Analysis, SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Scientific Computing, IMA Journal of Numerical Analysis, Pattern Recognition, Journal of Scientific Computing, Applied Numerical Mathematics, Data Mining and Knowledge Discovery, ACM Transactions on Information Systems等发表学术论文多篇。