Stochastic Principal Component Analysis Via Mean Absolute Projection Maximization
Stochastic Principal Component Analysis Via Mean Absolute Projection Maximization
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DOI：
10.1109/globalsip45357.2019.8969411
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
M. Dhanaraj;Panos P. Markopoulos
中科院分区：
文献类型：
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作者：
M. Dhanaraj;Panos P. Markopoulos
主成分分析（PCA）是一种数据处理方法，在信号处理和机器学习中有许多应用。同时，标准PCA已被证明对错误/离群数据非常敏感。另一方面，基于L1范数的PCA（L1-PCA），寻求最大化处理数据的总绝对投影，已表现出强大的抗腐败性。与此同时，在我们的大数据时代，需要在线（随机）算法来进行有限存储和计算需求的数据分析。为此，在本文中，我们扩展批L1-PCA，并提出了一种新的算法，随机PC计算的基础上平均绝对投影最大化，正式收敛保证。我们的数值研究表明，收敛性和证实所提出的方法的抗腐败性。
Principal-Component Analysis (PCA) is a data processing method with numerous applications in signal processing and machine learning. At the same time, standard PCA has been shown to be very sensitive against faulty/outlying data. On the other hand, L1-norm-based PCA (L1-PCA), seeking to maximize the aggregate absolute projections of the processed data, has demonstrated sturdy corruption resistance. At the same time, in our big data era, there is a need for online (stochastic) algorithms for data analysis with limited storage and computation requirements. To this end, in this paper we extend batch L1-PCA and propose a novel algorithm for stochastic PC calculation based on mean absolute projection maximization, with formal convergence guarantees. Our numerical studies demonstrate the convergence and corroborate the corruption resistance of the proposed method.