基于随机投影技术的矩阵填充算法的改进

利用随机投影加速技术将高维矩阵的奇异值分解(SVD)投影到一个低维子空间上进行,可以减少SVD消耗的时间。定义了奇异值随机投影压缩算子,取代之前的奇异值压缩算子,并用这个算子改进了定点连续(FPC)算法得到FPCrp算法。对改进前后的算法进行了大量实验,结果表明:随机投影技术能够在保持算法鲁棒性和精度的同时,节省50%以上的时间。因此,基于随机投影技术的矩阵填充算法更适合求解大规模问题。

Improvement of matrix completion algorithm based on random projection

Using random projection acceleration technology to project the Singular Value Decomposition (SVD) of higher dimensional matrices onto a lower subspace can reduce the time consumption of SVD. The singular value random projection compression operator was defined to replace the singular value compression operator, then it was used to improve the Fixed Point Continuation (FPC) algorithm and got FPCrp algorithm. Lots of experiments were conducted on the original algorithm and the improved one. The results show that the random projection technology can reduce more than 50% time consumption of the FPC algorithm, while maintaining its robustness and precision. The modified matrix completion algorithm based on random projection technology is effective in solving large scale problems.