Uncertainties in signal recovery from heterogeneous and convoluted time series with principal component analysis.

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Mariia Legenkaia, Laurent Bourdieu, Rémi Monasson
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引用次数: 0

Abstract

Principal component analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the quantity of data. We here investigate the impact of heterogeneities, often present in real data, on the reconstruction of low-dimensional trajectories and of their associated modes. We focus in particular on the effects of sample-to-sample fluctuations and of component-dependent temporal convolution and noise in the measurements. We derive analytical predictions for the error on the reconstructed trajectory and the confusion between the modes using the replica method in a high-dimensional setting, in which the number and the dimension of the data are comparable. We find in particular that sample-to-sample variability is deleterious for the reconstruction of the signal trajectory, but beneficial for the inference of the modes, and that the fluctuations in the temporal convolution kernels prevent perfect recovery of the latent modes even for very weak measurement noise. Our predictions are corroborated by simulations with synthetic data for a variety of control parameters.

用主成分分析从异构和卷积时间序列中恢复信号的不确定性。
主成分分析(PCA)是提取数据(特别是时间序列)的低维表示最常用的工具之一。众所周知,性能在很大程度上取决于数据的质量(噪声量)和数量。本文研究了实际数据中经常出现的异质性对低维轨迹及其相关模式重建的影响。我们特别关注样本对样本波动的影响以及测量中依赖于分量的时间卷积和噪声。在数据的数量和维数具有可比性的高维环境下,利用复制方法对重建轨迹的误差和模式之间的混淆进行了分析预测。我们特别发现,样本间的可变性对信号轨迹的重建是有害的,但对模态的推断是有益的,并且即使对于非常弱的测量噪声,时间卷积核的波动也会阻止潜在模态的完美恢复。我们的预测被各种控制参数的模拟合成数据所证实。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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