快速和可证明的张量鲁棒主成分分析通过缩放梯度下降

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-04-27 DOI:10.1093/imaiai/iaad019
Harry Dong, Tian Tong, Cong Ma, Yuejie Chi
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引用次数: 0

摘要

越来越多的数据科学和机器学习问题依赖于张量计算,它比矩阵更能捕捉数据的多方向关系和相互作用。当利用这一关键优势时,一个关键的挑战是开发计算效率高且可证明正确的算法,用于从张量数据中提取有用的信息,同时对损坏和病态具有鲁棒性。本文研究了张量鲁棒主成分分析(RPCA),其目的是在Tucker分解下从被稀疏腐蚀污染的观测中恢复低秩张量。为了最大限度地减少计算和内存占用,我们建议通过缩放梯度下降(ScaledGD)从定制谱初始化开始直接恢复低维张量因子,再加上迭代变化的阈值操作,以自适应地消除损坏的影响。从理论上讲,我们建立了该算法以与条件数无关的常数速率线性收敛到真正的低秩张量,只要破坏程度不太大。通过综合实验和实际应用,我们证明了所提出的算法比最先进的张量RPCA算法具有更好的可扩展性。
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Fast and provable tensor robust principal component analysis via scaled gradient descent
Abstract An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key challenge is to develop computationally efficient and provably correct algorithms for extracting useful information from tensor data that are simultaneously robust to corruptions and ill-conditioning. This paper tackles tensor robust principal component analysis (RPCA), which aims to recover a low-rank tensor from its observations contaminated by sparse corruptions, under the Tucker decomposition. To minimize the computation and memory footprints, we propose to directly recover the low-dimensional tensor factors—starting from a tailored spectral initialization—via scaled gradient descent (ScaledGD), coupled with an iteration-varying thresholding operation to adaptively remove the impact of corruptions. Theoretically, we establish that the proposed algorithm converges linearly to the true low-rank tensor at a constant rate that is independent with its condition number, as long as the level of corruptions is not too large. Empirically, we demonstrate that the proposed algorithm achieves better and more scalable performance than state-of-the-art tensor RPCA algorithms through synthetic experiments and real-world applications.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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