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.

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 Outlier Detection for Pandemic-Related Data Using Compositional Functional Data Analysis

2021 ◽  
pp. 251-266
Author(s):  
Christopher Rieser ◽  
Peter Filzmoser
Keyword(s):  
Outlier Detection ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Subject Area ◽  
Smooth Functions ◽  
Related Data ◽  
Relative Information ◽  
The Subject ◽  
Multivariate Functional Data ◽  
Events Data

AbstractWith accurate data, governments can make the most informed decisions to keep people safer through pandemics such as the COVID-19 coronavirus. In such events, data reliability is crucial and therefore outlier detection is an important and even unavoidable issue. Outliers are often considered as the most interesting observations, because the fact that they differ from the data majority may lead to relevant findings in the subject area. Outlier detection has also been addressed in the context of multivariate functional data, thus smooth functions of several characteristics, often derived from measurements at different time points (Hubert et al. in Stat Methods Appl 24(2):177–202, 2015b). Here the underlying data are regarded as compositions, with the compositional parts forming the multivariate information, and thus only relative information in terms of log-ratios between these parts is considered as relevant for the analysis. The multivariate functional data thus have to be derived as smooth functions by utilising this relative information. Subsequently, already established multivariate functional outlier detection procedures can be used, but for interpretation purposes, the functional data need to be presented in an appropriate space. The methodology is illustrated with publicly available data around the COVID-19 pandemic to find countries displaying outlying trends.

scholarly journals Functional Analysis of the Differences in the Dimensions of Two Types of Boiled and Steamed Rice Grains

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Mirosław Krzyśko ◽  
Waldemar Wołyński ◽  
Marek Domin ◽  
Zofia Hanusz ◽  
Leszek Rydzak ◽  
...  
Keyword(s):  
Heat Treatment ◽  
Functional Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Rice Grains ◽  
Cooking Process ◽  
Length Width ◽  
And Cluster Analysis ◽  
Multivariate Functional Data ◽  
The Impact

The study tested how the cooking process can change the dimensions of rice grains. The impact of set times of cooking or steaming process on the characteristics such as length, width, and height of two varieties of rice, namely, long-grain white and parboiled, was investigated. The measurements of the dimension characteristics obtained at different times of the cooking process were converted to functional data. Different methods of multivariate functional data analysis, namely, functional multivariate analysis of variance, functional discriminant coordinates, and cluster analysis, were applied to discover the differences between the two varieties and the two heat treatment methods.

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

Visualizing, clustering, and characterizing activity-trip sequences via weighted sequence alignment and functional data analysis

2021 ◽  
Vol 126 ◽  
pp. 103007
Author(s):  
Ying Song ◽  
Siyang Ren ◽  
Julian Wolfson ◽  
Yaxuan Zhang ◽  
Roland Brown ◽  
...  
Keyword(s):  
Data Analysis ◽  
Sequence Alignment ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Weighted Sequence

scholarly journals Novel Analytic Approaches to Investigate Minute-Level Actigraphy and Associations With Physical Function

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 194-195
Author(s):  
Kaiyuan Hua ◽  
Sheng Luo ◽  
Katherine Hall ◽  
Miriam Morey ◽  
Harvey Cohen
Keyword(s):  
Physical Activity ◽  
Data Analysis ◽  
Physical Function ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Gait Speed ◽  
Community Dwelling ◽  
Accelerometer Data ◽  
Single Leg Stance ◽  
Minute Walk

Abstract Background. Functional decline in conjunction with low levels of physical activity has implications for health risks in older adults. Previous studies have examined the associations between accelerometry-derived activity and physical function, but most of these studies reduced these data into average means of total daily physical activity (e.g., daily step counts). A new method of analysis “functional data analysis” provides more in-depth capability using minute-level accelerometer data. Methods. A secondary analysis of community-dwelling adults ages 30 to 90+ residing in southwest region of North Carolina from the Physical Performance across the Lifespan (PALS) study. PALS assessments were completed in-person at baseline and one-week of accelerometry. Final analysis includes 669 observations at baseline with minute-level accelerometer data from 7:00 to 23:00, after removing non-wear time. A novel scalar-on-function regression analysis was used to explore the associations between baseline physical activity features (minute-by-minute vector magnitude generated from accelerometer) and baseline physical function (gait speed, single leg stance, chair stands, and 6-minute walk test) with control for baseline age, sex, race and body mass index. Results. The functional regressions were significant for specific times of day indicating increased physical activity associated with increased physical function around 8:00, 9:30 and 15:30-17:00 for rapid gait speed; 9:00-10:30 and 15:00-16:30 for normal gait speed; 9:00-10:30 for single leg stance; 9:30-11:30 and 15:00-18:00 for chair stands; 9:00-11:30 and 15:00-18:30 for 6-minute walk. Conclusion. This method of functional data analysis provides news insights into the relationship between minute-by-minute daily activity and health.

A kNN procedure in semiparametric functional data analysis

2021 ◽  
pp. 109028
Author(s):  
Silvia Novo ◽  
Germán Aneiros ◽  
Philippe Vieu
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data
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