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Muehlmann C, De Iaco S, Nordhausen K. Blind recovery of sources for multivariate space-time random fields. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT : RESEARCH JOURNAL 2022; 37:1593-1613. [PMID: 37041981 PMCID: PMC10081984 DOI: 10.1007/s00477-022-02348-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 11/14/2022] [Indexed: 06/19/2023]
Abstract
With advances in modern worlds technology, huge datasets that show dependencies in space as well as in time occur frequently in practice. As an example, several monitoring stations at different geographical locations track hourly concentration measurements of a number of air pollutants for several years. Such a dataset contains thousands of multivariate observations, thus, proper statistical analysis needs to account for dependencies in space and time between and among the different monitored variables. To simplify the consequent multivariate spatio-temporal statistical analysis it might be of interest to detect linear transformations of the original observations that result in straightforward interpretative, spatio-temporally uncorrelated processes that are also highly likely to have a real physical meaning. Blind source separation (BSS) represents a statistical methodology which has the aim to recover so-called latent processes, that exactly meet the former requirements. BSS was already successfully used in sole temporal and sole spatial applications with great success, but, it was not yet introduced for the spatio-temporal case. In this contribution, a reasonable and innovative generalization of BSS for multivariate space-time random fields (stBSS), under second-order stationarity, is proposed, together with two space-time extensions of the well-known algorithms for multiple unknown signals extraction (stAMUSE) and the second-order blind identification (stSOBI) which solve the formulated problem. Furthermore, symmetry and separability properties of the model are elaborated and connections to the space-time linear model of coregionalization and to the classical principal component analysis are drawn. Finally, the usefulness of the new methods is shown in a thorough simulation study and on a real environmental application.
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Affiliation(s)
- C. Muehlmann
- Institute of Statistics and Mathematical Methods in Economics, TU Wien / Technische Universität Wien / Vienna University of Technology, Vienna, Austria
| | - S. De Iaco
- Department of Economic Sciences-Sect. of Mathematics and Statistics, University of Salento, Lecce, Italy
- Centro Nazionale di Biodiversità, University of Salento, Lecce, Italy
| | - K. Nordhausen
- Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland
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Zangeneh Soroush M, Tahvilian P, Nasirpour MH, Maghooli K, Sadeghniiat-Haghighi K, Vahid Harandi S, Abdollahi Z, Ghazizadeh A, Jafarnia Dabanloo N. EEG artifact removal using sub-space decomposition, nonlinear dynamics, stationary wavelet transform and machine learning algorithms. Front Physiol 2022; 13:910368. [PMID: 36091378 PMCID: PMC9449652 DOI: 10.3389/fphys.2022.910368] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 07/11/2022] [Indexed: 11/22/2022] Open
Abstract
Blind source separation (BSS) methods have received a great deal of attention in electroencephalogram (EEG) artifact elimination as they are routine and standard signal processing tools to remove artifacts and reserve desired neural information. On the other hand, a classifier should follow BSS methods to automatically identify artifactual sources and remove them in the following steps. In addition, removing all detected artifactual components leads to loss of information since some desired information related to neural activity leaks to these sources. So, an approach should be employed to detect and suppress the artifacts and reserve neural activity. This study introduces a novel method based on EEG and Poincare planes in the phase space to detect artifactual components estimated by second-order blind identification (SOBI). Artifacts are detected using a mixture of well-known conventional classifiers and were removed employing stationary wavelet transform (SWT) to reserve neural information. The proposed method is a combination of signal processing techniques and machine learning algorithms, including multi-layer perceptron (MLP), K-nearest neighbor (KNN), naïve Bayes, and support vector machine (SVM) which have significant results while applying our proposed method to different scenarios. Simulated, semi-simulated, and real EEG signals are employed to evaluate the proposed method, and several evaluation criteria are calculated. We achieved acceptable results, for example, 98% average accuracy and 97% average sensitivity in artifactual EEG component detection or about 2% as mean square error in EEG reconstruction after artifact removal. Results showed that the proposed method is effective and can be used in future studies as we have considered different real-world scenarios to evaluate it.
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Affiliation(s)
- Morteza Zangeneh Soroush
- Occupational Sleep Research Center, Baharloo Hospital, Tehran University of Medical Sciences, Tehran, Iran
- School of Cognitive Sciences, Institute for Research in Fundamental Sciences, IPM, Tehran, Iran
- Bio-Intelligence Research Unit, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran
- Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
- Engineering Research Center in Medicine and Biology, Science and Research Branch, Islamic Azad University, Tehran, Iran
- Department of Clinical Neuroscience, Mahdiyeh Clinic, Tehran, Iran
- *Correspondence: Morteza Zangeneh Soroush,
| | - Parisa Tahvilian
- Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
- Engineering Research Center in Medicine and Biology, Science and Research Branch, Islamic Azad University, Tehran, Iran
| | - Mohammad Hossein Nasirpour
- Department of Medical Genetics, Institute of Medical Biotechnology, National Institute of Genetic Engineering and Biotechnology (NIGEB), Tehran, Iran
| | - Keivan Maghooli
- Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
- Engineering Research Center in Medicine and Biology, Science and Research Branch, Islamic Azad University, Tehran, Iran
| | - Khosro Sadeghniiat-Haghighi
- Occupational Sleep Research Center, Baharloo Hospital, Tehran University of Medical Sciences, Tehran, Iran
- Sleep Breathing Disorders Research Center, Tehran University of Medical Sciences, Tehran, Iran
| | - Sepide Vahid Harandi
- Department of Psychology, Islamic Azad University, Najafabad Branch, Najafabad, Iran
| | - Zeinab Abdollahi
- Department of Electrical and Computer Engineering, Islamic Azad University, Qazvin Branch, Qazvin, Iran
| | - Ali Ghazizadeh
- School of Cognitive Sciences, Institute for Research in Fundamental Sciences, IPM, Tehran, Iran
- Bio-Intelligence Research Unit, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran
| | - Nader Jafarnia Dabanloo
- Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
- Engineering Research Center in Medicine and Biology, Science and Research Branch, Islamic Azad University, Tehran, Iran
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Pan Y, Matilainen M, Taskinen S, Nordhausen K. A review of second-order blind identification methods. WILEY INTERDISCIPLINARY REVIEWS. COMPUTATIONAL STATISTICS 2022; 14:e1550. [PMID: 36249858 PMCID: PMC9540980 DOI: 10.1002/wics.1550] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2020] [Revised: 01/06/2021] [Accepted: 01/07/2021] [Indexed: 11/24/2022]
Abstract
Second-order source separation (SOS) is a data analysis tool which can be used for revealing hidden structures in multivariate time series data or as a tool for dimension reduction. Such methods are nowadays increasingly important as more and more high-dimensional multivariate time series data are measured in numerous fields of applied science. Dimension reduction is crucial, as modeling such high-dimensional data with multivariate time series models is often impractical as the number of parameters describing dependencies between the component time series is usually too high. SOS methods have their roots in the signal processing literature, where they were first used to separate source signals from an observed signal mixture. The SOS model assumes that the observed time series (signals) is a linear mixture of latent time series (sources) with uncorrelated components. The methods make use of the second-order statistics-hence the name "second-order source separation." In this review, we discuss the classical SOS methods and their extensions to more complex settings. An example illustrates how SOS can be performed. This article is categorized under:Statistical Models > Time Series ModelsStatistical and Graphical Methods of Data Analysis > Dimension ReductionData: Types and Structure > Time Series, Stochastic Processes, and Functional Data.
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Affiliation(s)
- Yan Pan
- Department of Mathematics and StatisticsUniversity of JyväskyläFinland
| | - Markus Matilainen
- Turku PET CentreTurku University Hospital and University of TurkuFinland
| | - Sara Taskinen
- Department of Mathematics and StatisticsUniversity of JyväskyläFinland
| | - Klaus Nordhausen
- Department of Mathematics and StatisticsUniversity of JyväskyläFinland
- Institute of Statistics and Mathematical Methods in Economics, TUViennaAustria
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Miettinen J, Matilainen M, Nordhausen K, Taskinen S. Extracting Conditionally Heteroskedastic Components using Independent Component Analysis. JOURNAL OF TIME SERIES ANALYSIS 2020; 41:293-311. [PMID: 32508370 PMCID: PMC7266430 DOI: 10.1111/jtsa.12505] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/21/2018] [Revised: 08/12/2019] [Accepted: 08/13/2019] [Indexed: 06/11/2023]
Abstract
In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In this article, we study an ICA method which combines the use of linear and quadratic autocorrelations to enable efficient estimation of various kinds of stationary time series. Statistical properties of the estimator are studied by finding its limiting distribution under general conditions, and the asymptotic variances are derived in the case of ARMA-GARCH model. We use the asymptotic results and a finite sample simulation study to compare different choices of a weight coefficient. As it is often of interest to identify all those components which exhibit stochastic volatility features we suggest a test statistic for this problem. We also show that a slightly modified version of the principal volatility component analysis can be seen as an ICA method. Finally, we apply the estimators in analysing a data set which consists of time series of exchange rates of seven currencies to US dollar. Supporting information including proofs of the theorems is available online.
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Affiliation(s)
- Jari Miettinen
- Department of Signal Processing and AcousticsAalto UniversityHelsinkiFinland
| | - Markus Matilainen
- Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland
- Turku PET CentreTurku University Hospital and University of TurkuFinland
| | - Klaus Nordhausen
- Institute of Statistics & Mathematical Methods in EconomicsVienna University of TechnologyWienAustria
| | - Sara Taskinen
- Department of Mathematics and StatisticsUniversity of JyvaskylaJyväskyläFinland
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Bachoc F, Genton MG, Nordhausen K, Ruiz-Gazen A, Virta J. Spatial blind source separation. Biometrika 2020. [DOI: 10.1093/biomet/asz079] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Summary
Recently a blind source separation model was suggested for spatial data, along with an estimator based on the simultaneous diagonalization of two scatter matrices. The asymptotic properties of this estimator are derived here, and a new estimator based on the joint diagonalization of more than two scatter matrices is proposed. The asymptotic properties and merits of the novel estimator are verified in simulation studies. A real-data example illustrates application of the method.
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Affiliation(s)
- François Bachoc
- Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
| | - Marc G Genton
- Statistics Program, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
| | - Klaus Nordhausen
- Computational Statistics, Vienna University of Technology, Wiedner Hauptstr. 7, A-1040 Vienna, Austria
| | - Anne Ruiz-Gazen
- Toulouse School of Economics, University of Toulouse Capitole, 1, Esplanade de l’Université, 31080 Toulouse Cedex 06, France
| | - Joni Virta
- Department of Mathematics and Statistics, University of Turku, 20014 Turun yliopisto, Finland
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