基于谱正则化算法的大数据矩阵完备化研究

摘要

Matrix completion is based on the observed data to complete the forecast problem of the matrix. Now, with the devel-opment of Internet technology, the time of big data is coming, but the most data in the big data matrix is still blank, and need to supplement. Namely, it is matrix completion problem of big data. The spectral regularization model is used to solve the matrix completion problem of big data. This model turns matrix completion problem into nuclear regularized least squares problem. And the series of regularization low-rank solution are given by the truncated singular value decomposition using the convex relaxation technique. The experimental results of the Netflix big data proved the proposed method.%矩阵完备化是基于部分观测数据来完成全部矩阵预测的问题。随着互联网技术的发展，大数据时代的来临，大数据矩阵中大多数据依然是空白的，需要补充，即大数据存在矩阵完备化的问题。本文利用谱正则化模型和算法来解决大数据的矩阵完备化问题，该方法将矩阵完备化问题整理成核范数最小二乘问题，再通过截断奇异值分解、软输入算法和硬输入算法给出了一系列正则化低秩解。最后基于实际的Netflix大数据的实验结果证明了本文的方法。