The registration and display of functional data

1997 ◽  
pp. 67-83 ◽  
Author(s):  
J. O. Ramsay ◽  
B. W. Silverman
Keyword(s):  
Functional Data

scholarly journals Bounding uncertainty in functional data: A case study

2021 ◽  
Vol 33 (1) ◽  
pp. 178-188
Author(s):  
Caleb King ◽  
Nevin Martin ◽  
James Derek Tucker
Keyword(s):  
Functional Data

scholarly journals Advanced Statistical Analysis of 3D Kinect Data: Mimetic Muscle Rehabilitation Following Head and Neck Surgeries Causing Facial Paresis

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 103
Author(s):  
Jan Kohout ◽  
Ludmila Verešpejová ◽  
Pavel Kříž ◽  
Lenka Červená ◽  
Karel Štícha ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Functional Data ◽  
Muscle Function ◽  
Evaluation Process ◽  
Multiple Logistic Regression ◽  
Facial Paresis ◽  
Kinect Camera ◽  
3D Camera ◽  
Mimetic Muscles ◽  
Data Analytic

An advanced statistical analysis of patients’ faces after specific surgical procedures that temporarily negatively affect the patient’s mimetic muscles is presented. For effective planning of rehabilitation, which typically lasts several months, it is crucial to correctly evaluate the improvement of the mimetic muscle function. The current way of describing the development of rehabilitation depends on the subjective opinion and expertise of the clinician and is not very precise concerning when the most common classification (House–Brackmann scale) is used. Our system is based on a stereovision Kinect camera and an advanced mathematical approach that objectively quantifies the mimetic muscle function independently of the clinician’s opinion. To effectively deal with the complexity of the 3D camera input data and uncertainty of the evaluation process, we designed a three-stage data-analytic procedure combining the calculation of indicators determined by clinicians with advanced statistical methods including functional data analysis and ordinal (multiple) logistic regression. We worked with a dataset of 93 distinct patients and 122 sets of measurements. In comparison to the classification with the House–Brackmann scale the developed system is able to automatically monitor reinnervation of mimetic muscles giving us opportunity to discriminate even small improvements during the course of rehabilitation.

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.

scholarly journals Associations between Google Search Trends for Symptoms and COVID-19 Confirmed and Death Cases in the United States

2021 ◽  
Vol 18 (9) ◽  
pp. 4560
Author(s):  
Mostafa Abbas ◽  
Thomas B. Morland ◽  
Eric S. Hall ◽  
Yasser EL-Manzalawy
Keyword(s):  
Functional Data ◽  
Time Series Data ◽  
Principal Component ◽  
State Level ◽  
The United States ◽  
Functional Principal Component Analysis ◽  
Series Data ◽  
Dynamic Correlation ◽  
The Us ◽  
Google Search

We utilize functional data analysis techniques to investigate patterns of COVID-19 positivity and mortality in the US and their associations with Google search trends for COVID-19-related symptoms. Specifically, we represent state-level time series data for COVID-19 and Google search trends for symptoms as smoothed functional curves. Given these functional data, we explore the modes of variation in the data using functional principal component analysis (FPCA). We also apply functional clustering analysis to identify patterns of COVID-19 confirmed case and death trajectories across the US. Moreover, we quantify the associations between Google COVID-19 search trends for symptoms and COVID-19 confirmed case and death trajectories using dynamic correlation. Finally, we examine the dynamics of correlations for the top nine Google search trends of symptoms commonly associated with COVID-19 confirmed case and death trajectories. Our results reveal and characterize distinct patterns for COVID-19 spread and mortality across the US. The dynamics of these correlations suggest the feasibility of using Google queries to forecast COVID-19 cases and mortality for up to three weeks in advance. Our results and analysis framework set the stage for the development of predictive models for forecasting COVID-19 confirmed cases and deaths using historical data and Google search trends for nine symptoms associated with both outcomes.

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