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

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

2018 ◽  
Vol 8 (10) ◽  
pp. 1766 ◽  
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.

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 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 Subpopulation identification for single-cell RNA-sequencing data using functional data analysis

2019 ◽  
Author(s):  
Kyungmin Ahn ◽  
Hironobu Fujiwara
Keyword(s):  
Gene Expression ◽  
Data Analysis ◽  
Single Cell ◽  
Gene Expression Data ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Clustering Algorithms ◽  
Expression Data ◽  
Clustering Methods ◽  
Single Cell Rna Sequencing

AbstractBackgroundIn single-cell RNA-sequencing (scRNA-seq) data analysis, a number of statistical tools in multivariate data analysis (MDA) have been developed to help analyze the gene expression data. This MDA approach is typically focused on examining discrete genomic units of genes that ignores the dependency between the data components. In this paper, we propose a functional data analysis (FDA) approach on scRNA-seq data whereby we consider each cell as a single function. To avoid a large number of dropouts (zero or zero-closed values) and reduce the high dimensionality of the data, we first perform a principal component analysis (PCA) and assign PCs to be the amplitude of the function. Then we use the index of PCs directly from PCA for the phase components. This approach allows us to apply FDA clustering methods to scRNA-seq data analysis.ResultsTo demonstrate the robustness of our method, we apply several existing FDA clustering algorithms to the gene expression data to improve the accuracy of the classification of the cell types against the conventional clustering methods in MDA. As a result, the FDA clustering algorithms achieve superior accuracy on simulated data as well as real data such as human and mouse scRNA-seq data.ConclusionsThis new statistical technique enhances the classification performance and ultimately improves the understanding of stochastic biological processes. This new framework provides an essentially different scRNA-seq data analytical approach, which can complement conventional MDA methods. It can be truly effective when current MDA methods cannot detect or uncover the hidden functional nature of the gene expression dynamics.

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

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
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