Clustering Multivariate Functional Data with Phase Variation

Park, Juhyun; Ahn, Jeongyoun

doi:10.1111/biom.12546

Cited by 40 publications

(26 citation statements)

References 32 publications

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“…In addition to FPCA, there are also abundant literatures on models for multivariate functional data with most focusing on dense functional data. For clustering of multivariate functional data, see Zhu, Brown, and Morris (), Jacques and Preda (), Huang, Li, and Guan (), and Park and Ahn (). For regression with multivariate functional responses, see Zhu et al.…”

Section: Introductionmentioning

confidence: 99%

Fast covariance estimation for multivariate sparse functional data

Xiao

Luo

2020

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Covariance estimation is essential yet underdeveloped for analysing multivariate functional data. We propose a fast covariance estimation method for multivariate sparse functional data using bivariate penalized splines. The tensor‐product B‐spline formulation of the proposed method enables a simple spectral decomposition of the associated covariance operator and explicit expressions of the resulting eigenfunctions as linear combinations of B‐spline bases, thereby dramatically facilitating subsequent principal component analysis. We derive a fast algorithm for selecting the smoothing parameters in covariance smoothing using leave‐one‐subject‐out cross‐validation. The method is evaluated with extensive numerical studies and applied to an Alzheimer's disease study with multiple longitudinal outcomes.

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Section: Introductionmentioning

confidence: 99%

Fast covariance estimation for multivariate sparse functional data

Xiao

Luo

2020

Stat

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“…Recently, [ 16 ] and [ 17 ] considered quantile contour estimation of functional principal components (FPC) with emphasis on analysis for growth curves, but only with a single growth trajectory sample. In a related approach, [ 18 ] focused on finding subjective-specific warping functions to extract common features among multivariate growth traits. In contrast to existing approaches, we profile multiple growth patterns in terms of archetypal analysis [ 19 – 21 ], where we implicitly assume that extreme growth patterns can be used to represent individual growth curves in the sample through convex combination.…”

Section: Introductionmentioning

confidence: 99%

Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development

et al. 2018

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For longitudinal studies with multivariate observations, we propose statistical methods to identify clusters of archetypal subjects by using techniques from functional data analysis and to relate longitudinal patterns to outcomes. We demonstrate how this approach can be applied to examine associations between multiple time-varying exposures and subsequent health outcomes, where the former are recorded sparsely and irregularly in time, with emphasis on the utility of multiple longitudinal observations in the framework of dimension reduction techniques. In applications to children’s growth data, we investigate archetypes of infant growth patterns and identify subgroups that are related to cognitive development in childhood. Specifically, “Stunting” and “Faltering” time-dynamic patterns of head circumference, body length and weight in the first 12 months are associated with lower levels of long-term cognitive development in comparison to “Generally Large” and “Catch-up” growth. Our findings provide evidence for the statistical association between multivariate growth patterns in infancy and long-term cognitive development.

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“…A robust clustering algorithm for stationary FTS was introduced in [36]. Finally, current efforts are directed towards the development of clustering algorithms for multivariate functional data [7,[37][38][39].…”

Section: Related Workmentioning

confidence: 99%

A Novel Hybrid Algorithm to Forecast Functional Time Series Based on Pattern Sequence Similarity with Application to Electricity Demand

et al. 2018

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The forecasting of future values is a very challenging task. In almost all scientific disciplines, the analysis of time series provides useful information and even economic benefits. In this context, this paper proposes a novel hybrid algorithm to forecast functional time series with arbitrary prediction horizons. It integrates a well-known clustering functional data algorithm into a forecasting strategy based on pattern sequence similarity, which was originally developed for discrete time series. The new approach assumes that some patterns are repeated over time, and it attempts to discover them and evaluate their immediate future. Hence, the algorithm first applies a clustering functional time series algorithm, i.e., it assigns labels to every data unit (it may represent either one hour, or one day, or any arbitrary length). As a result, the time series is transformed into a sequence of labels. Later, it retrieves the sequence of labels occurring just after the sample that we want to be forecasted. This sequence is searched for within the historical data, and every time it is found, the sample immediately after is stored. Once the searching process is terminated, the output is generated by weighting all stored data. The performance of the approach has been tested on real-world datasets related to electricity demand and compared to other existing methods, reporting very promising results. Finally, a statistical significance test has been carried out to confirm the suitability of the election of the compared methods. In conclusion, a novel algorithm to forecast functional time series is proposed with very satisfactory results when assessed in the context of electricity demand.

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Clustering Multivariate Functional Data with Phase Variation

Cited by 40 publications

References 32 publications

Fast covariance estimation for multivariate sparse functional data

Fast covariance estimation for multivariate sparse functional data

Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development

A Novel Hybrid Algorithm to Forecast Functional Time Series Based on Pattern Sequence Similarity with Application to Electricity Demand

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