A new method to improve the efficiency and accuracy of incremental singular value decomposition

IF 0.7 4区 数学 Q2 Mathematics
Hansi Jiang, A. Chaudhuri
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引用次数: 0

Abstract

Singular value decomposition (SVD) has been widely used in machine learning. It lies at the root of data analysis, and it provides the mathematical basis for many data mining techniques. Recently, interest in incremental SVD has been on the rise because it is well suited to streaming data. In this paper, we propose a new algorithm of incremental SVD that is designed to improve both efficiency and accuracy during computation. More specifically, our proposed algorithm takes advantage of the special structures of arrowhead and diagonal-plus-rank-one matrices involved in updating SVD models to expedite the updating process. Moreover, because the singular values are computed independently, the proposed method can be easily parallelized. In addition, as this paper shows, increasing rank can lead to more accurate singular values in the updating process. Experimental results from synthetic and real data sets demonstrate gains in efficiency and accuracy in the updating process.
一种提高增量奇异值分解效率和精度的新方法
奇异值分解(SVD)在机器学习中得到了广泛的应用。它是数据分析的基础,为许多数据挖掘技术提供了数学基础。最近,对增量SVD的兴趣一直在上升,因为它非常适合流式数据。在本文中,我们提出了一种新的增量SVD算法,该算法旨在提高计算的效率和准确性。更具体地说,我们提出的算法利用了SVD模型更新中涉及的箭头和对角线加秩一矩阵的特殊结构来加快更新过程。此外,由于奇异值是独立计算的,因此所提出的方法可以很容易地并行化。此外,正如本文所示,增加秩可以在更新过程中获得更准确的奇异值。来自合成数据集和真实数据集的实验结果表明,在更新过程中提高了效率和准确性。
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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