scholarly journals Clustering multivariate functional data in group-specific functional subspaces

2020 ◽  
Vol 35 (3) ◽  
pp. 1101-1131
Author(s):  
Amandine Schmutz ◽  
Julien Jacques ◽  
Charles Bouveyron ◽  
Laurence Chèze ◽  
Pauline Martin
Keyword(s):  
Functional Data ◽  
Multivariate Functional Data

scholarly journals Conformal Prediction bands for multivariate functional data

2021 ◽  
pp. 104879
Author(s):  
Jacopo Diquigiovanni ◽  
Matteo Fontana ◽  
Simone Vantini
Keyword(s):  
Functional Data ◽  
Conformal Prediction ◽  
Multivariate Functional Data ◽  
Prediction Bands

scholarly journals Spatiotemporal Prediction of COVID-19 Mortality and Risk Assessment

2020 ◽  
Author(s):  
Antoni Torres-Signes ◽  
M. Pilar Frías ◽  
María D.Ruiz-Medina
Keyword(s):  
Mortality Risk ◽  
Functional Data ◽  
Statistical Approach ◽  
Model Fitting ◽  
Functional Regression ◽  
Infinite Dimensional ◽  
Trend Model ◽  
Risk Forecasting ◽  
Model Ranking ◽  
Multivariate Functional Data

Abstract This paper presents a multivariate functional data statistical approach, for spatiotemporal prediction of COVID-19 mortality counts. Specifically, spatial heterogeneous nonlinear parametric functional regression trend model fitting is first implemented. Classical and Bayesian infinite-dimensional log-Gaussian linear residual correlation analysis is then applied. The nonlinear regression predictor of the mortality risk is combined with the plug-in predictor of the multiplicative error term. An empirical model ranking, based on random K-fold validation, is established for COVID-19 mortality risk forecasting and assessment, involving Machine Learning (ML) models, and the adopted Classical and Bayesian semilinear estimation approach. This empirical analysis also determines the ML models favored by the spatial multivariate Functional Data Analysis (FDA) framework. The results could be extrapolated to other countries.

scholarly journals A New Functional Clustering Method with Combined Dissimilarity Sources and Graphical Interpretation

2021 ◽  
Author(s):  
Wenlin Dai ◽  
Stavros Athanasiadis ◽  
Tomáš Mrkvička
Keyword(s):  
Functional Data Analysis ◽  
Functional Data ◽  
Visualization Tool ◽  
Functional Clustering ◽  
Graphical Interpretation ◽  
Model Free ◽  
Heavy Tailed ◽  
Cluster Variation ◽  
And Performance ◽  
Multivariate Functional Data

Clustering is an essential task in functional data analysis. In this study, we propose a framework for a clustering procedure based on functional rankings or depth. Our methods naturally combine various types of between-cluster variation equally, which caters to various discriminative sources of functional data; for example, they combine raw data with transformed data or various components of multivariate functional data with their covariance. Our methods also enhance the clustering results with a visualization tool that allows intrinsic graphical interpretation. Finally, our methods are model-free and nonparametric and hence are robust to heavy-tailed distribution or potential outliers. The implementation and performance of the proposed methods are illustrated with a simulation study and applied to three real-world applications.

Discriminant coordinates analysis for multivariate functional data

2019 ◽  
Vol 49 (18) ◽  
pp. 4506-4519
Author(s):  
Zofia Hanusz ◽  
Mirosław Krzyśko ◽  
Rafał Nadulski ◽  
Łukasz Waszak
Keyword(s):  
Functional Data ◽  
Multivariate Functional Data

Crisp and fuzzy k-means clustering algorithms for multivariate functional data

2007 ◽  
Vol 22 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Shuichi Tokushige ◽  
Hiroshi Yadohisa ◽  
Koichi Inada
Keyword(s):  
Functional Data ◽  
Clustering Algorithms ◽  
Multivariate Functional Data

Simplicial band depth for multivariate functional data

2014 ◽  
Vol 8 (3) ◽  
pp. 321-338 ◽  
Author(s):  
Sara López-Pintado ◽  
Ying Sun ◽  
Juan K. Lin ◽  
Marc G. Genton
Keyword(s):  
Functional Data ◽  
Multivariate Functional Data ◽  
Band Depth

scholarly journals Use of Depth Measure for Multivariate Functional Data in Disease Prediction: An Application to Electrocardiograph Signals

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Nicholas Tarabelloni ◽  
Francesca Ieva ◽  
Rachele Biasi ◽  
Anna Maria Paganoni
Keyword(s):  
Functional Data ◽  
Simulation Studies ◽  
Bundle Branch Block ◽  
Ecg Signals ◽  
Covariance Operators ◽  
Multivariate Functional Data ◽  
Nonparametric Comparison ◽  
Two Populations ◽  
Generalized Regression Model

AbstractIn this paper we develop statistical methods to compare two independent samples of multivariate functional data that differ in terms of covariance operators. In particular we generalize the concept of depth measure to this kind of data, exploiting the role of the covariance operators in weighting the components that define the depth. Two simulation studies are carried out to validate the robustness of the proposed methods and to test their effectiveness in some settings of interest. We present an application to Electrocardiographic (ECG) signals aimed at comparing physiological subjects and patients affected by Left Bundle Branch Block. The proposed depth measures computed on data are then used to perform a nonparametric comparison test among these two populations. They are also introduced into a generalized regression model aimed at classifying the ECG signals.

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