A generalization of functional clustering for discrete multivariate longitudinal data

This paper presents a new model-based generalized functional clustering method for discrete longitudinal data, such as multivariate binomial and Poisson distributed data. For this purpose, we propose a multivariate functional principal component analysis (MFPCA)-based clustering procedure for a latent multivariate Gaussian process instead of the original functional data directly. The main contribution of this study is two-fold: modeling of discrete longitudinal data with the latent multivariate Gaussian process and developing of a clustering algorithm based on MFPCA coupled with the latent multivariate Gaussian process. Numerical experiments, including real data analysis and a simulation study, demonstrate the promising empirical properties of the proposed approach.

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Robust functional clustering of ERP data with application to a study of implicit learning in autism

Biostatistics ◽

10.1093/biostatistics/kxw002 ◽

2016 ◽

Vol 17 (3) ◽

pp. 484-498 ◽

Cited By ~ 5

Author(s):

Kyle Hasenstab ◽

Catherine Sugar ◽

Donatello Telesca ◽

Shafali Jeste ◽

Damla Şentürk

Keyword(s):

Implicit Learning ◽

Clustering Algorithm ◽

Signal To Noise Ratio ◽

Principal Component ◽

Autism Spectrum ◽

Event Related Potential ◽

Functional Principal Component Analysis ◽

Sliding Windows ◽

Cluster Membership ◽

Functional Clustering

Abstract Motivated by a study on visual implicit learning in young children with Autism Spectrum Disorder (ASD), we propose a robust functional clustering (RFC) algorithm to identify subgroups within electroencephalography (EEG) data. The proposed RFC is an iterative algorithm based on functional principal component analysis, where cluster membership is updated via predictions of the functional trajectories obtained through a non-parametric random effects model. We consider functional data resulting from event-related potential (ERP) waveforms representing EEG time-locked to stimuli over the course of an implicit learning experiment, after applying a previously proposed meta-preprocessing step. This meta-preprocessing is designed to increase the low signal-to-noise ratio in the raw data and to mitigate the longitudinal changes in the ERP waveforms which characterize the nature and speed of learning. The resulting functional ERP components (peak amplitudes and latencies) inherently exhibit covariance heterogeneity due to low data quality over some stimuli inducing the averaging of different numbers of waveforms in sliding windows of the meta-preprocessing step. The proposed RFC algorithm incorporates this known covariance heterogeneity into the clustering algorithm, improving cluster quality, as illustrated in the data application and extensive simulation studies. ASD is a heterogeneous syndrome and identifying subgroups within ASD children is of interest for understanding the diverse nature of this complex disorder. Applications to the implicit learning paradigm identify subgroups within ASD and typically developing children with diverse learning patterns over the course of the experiment, which may inform clinical stratification of ASD.

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Separation of Chromatographic Co-Eluted Compounds by Clustering and by Functional Data Analysis

Metabolites ◽

10.3390/metabo11040214 ◽

2021 ◽

Vol 11 (4) ◽

pp. 214

Author(s):

Aneta Sawikowska ◽

Anna Piasecka ◽

Piotr Kachlicki ◽

Paweł Krajewski

Keyword(s):

Simulated Data ◽

Principal Component ◽

Real Data ◽

Functional Principal Component Analysis ◽

Additional Advantage ◽

Time Alignment ◽

Peak Separation ◽

Biological Mixtures ◽

Overlapping Peaks ◽

Retention Time Alignment

Peak overlapping is a common problem in chromatography, mainly in the case of complex biological mixtures, i.e., metabolites. Due to the existence of the phenomenon of co-elution of different compounds with similar chromatographic properties, peak separation becomes challenging. In this paper, two computational methods of separating peaks, applied, for the first time, to large chromatographic datasets, are described, compared, and experimentally validated. The methods lead from raw observations to data that can form inputs for statistical analysis. First, in both methods, data are normalized by the mass of sample, the baseline is removed, retention time alignment is conducted, and detection of peaks is performed. Then, in the first method, clustering is used to separate overlapping peaks, whereas in the second method, functional principal component analysis (FPCA) is applied for the same purpose. Simulated data and experimental results are used as examples to present both methods and to compare them. Real data were obtained in a study of metabolomic changes in barley (Hordeum vulgare) leaves under drought stress. The results suggest that both methods are suitable for separation of overlapping peaks, but the additional advantage of the FPCA is the possibility to assess the variability of individual compounds present within the same peaks of different chromatograms.

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Multi-model multivariate Gaussian process modelling with correlated noises

Journal of Process Control ◽

10.1016/j.jprocont.2017.08.004 ◽

2017 ◽

Vol 58 ◽

pp. 11-22 ◽

Cited By ~ 8

Author(s):

Xiaodan Hong ◽

Biao Huang ◽

Yongsheng Ding ◽

Fan Guo ◽

Lei Chen ◽

...

Keyword(s):

Gaussian Process ◽

Process Modelling ◽

Multivariate Gaussian ◽

Multivariate Gaussian Process ◽

Correlated Noises

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Functional Data Analysis in Sport Science: Example of Swimmers’ Progression Curves Clustering

Applied Sciences ◽

10.3390/app8101766 ◽

2018 ◽

Vol 8 (10) ◽

pp. 1766 ◽

Cited By ~ 2

Author(s):

Arthur Leroy ◽

Andy MARC ◽

Olivier DUPAS ◽

Jean Lionel REY ◽

Servane Gey

Keyword(s):

Data Analysis ◽

Functional Data Analysis ◽

Functional Data ◽

Clustering Algorithms ◽

Principal Component ◽

Continuous Functions ◽

Functional Principal Component Analysis ◽

Data Set ◽

Functional Clustering ◽

Sport Science

Many data collected in sport science come from time dependent phenomenon. This article focuses on Functional Data Analysis (FDA), which study longitudinal data by modelling them as continuous functions. After a brief review of several FDA methods, some useful practical tools such as Functional Principal Component Analysis (FPCA) or functional clustering algorithms are presented and compared on simulated data. Finally, the problem of the detection of promising young swimmers is addressed through a curve clustering procedure on a real data set of performance progression curves. This study reveals that the fastest improvement of young swimmers generally appears before 16 years old. Moreover, several patterns of improvement are identified and the functional clustering procedure provides a useful detection tool.

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Simulation Optimization for Computer Models With Multivariate Output

Volume 4: Bio and Sustainable Manufacturing ◽

10.1115/msec2017-2907 ◽

2017 ◽

Author(s):

Raed Kontar ◽

Shiyu Zhou ◽

John Horst

Keyword(s):

Gaussian Process ◽

Manufacturing Systems ◽

Performance Metrics ◽

Simulation Optimization ◽

Process Models ◽

Manufacturing Performance ◽

Gaussian Process Models ◽

Multivariate Gaussian ◽

Potential Applicability ◽

Multivariate Gaussian Process

This paper explores the potential of Gaussian process based Metamodels for simulation optimization with multivariate outputs. Specifically we focus on Multivariate Gaussian process models established through separable and non-separable covariance structures. We discuss the advantages and drawbacks of each approach and their potential applicability in manufacturing systems. The advantageous features of the Multivariate Gaussian process models are then demonstrated in a case study for the optimization of manufacturing performance metrics.

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