Representing functional data as smooth functions

1997 ◽  
pp. 37-56
Author(s):  
J. O. Ramsay ◽  
B. W. Silverman
Keyword(s):  
Functional Data ◽  
Smooth Functions

scholarly journals Application of functional data analysis to classify communities according to the pattern of malaria incidence, to guide targeted control strategies.

2020 ◽  
Author(s):  
Sokhna DIENG ◽  
Pierre Michel ◽  
Abdoulaye Guindo ◽  
Kankoe Sallah ◽  
El-hadj Ba ◽  
...  
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Temporal Pattern ◽  
Malaria Incidence ◽  
Smooth Functions ◽  
High Incidence ◽  
Incidence Pattern ◽  
Low Incidence

Abstract Background Effective targeting of malaria control in low transmission areas requires identification of transmission foci or hotspots. We investigated the use of functional data analysis to identify and describe spatio-temporal pattern of malaria incidence in an area with seasonal transmission in west-central Senegal. Method Malaria surveillance was maintained over 5 years from 2008 to 2012 at health facilities serving a population of 500,000 in 575 villages in two health districts in Senegal. Smooth functions were fitted from the time series of malaria incidence for each village, using cubic B-spline basis functions. The resulting smooth functions for each village were classified using hierarchical clustering (Ward’s method), using several different dissimilarity measures. The optimal number of clusters was then determined based on four cluster validity indices, to determine the main types of distinct temporal pattern of malaria incidence. Epidemiological indicators characterizing the resulting malaria incidence pattern in terms of the timing of seasonal outbreaks, were calculated based on the slope (velocity) and rate of change of the slope (acceleration) of the incidence over time. Results Three distinct patterns of malaria incidence were identified. A pattern characterized by high incidence, in 12/575 (2%) villages, with average incidence of 114 cases/1000 person-years over the 5 year study period; a pattern with intermediate incidence in 97 villages (17%), with average incidence of 13 cases/1000 person-years; and a pattern with low incidence in 466 (81%) villages, with average incidence 2.6 cases/1000 person-years. Epidemiological indicators characterizing the fluctuations in malaria incidence showed that seasonal outbreaks started later, and ended earlier, in the low incidence pattern. Conclusion Functional data analysis can be used to classify communities based on time series of malaria incidence, and to identify high incidence communities. Indicators can be derived from the fitted functions which characterize the timing of outbreaks. These tools may help to better target control measures.

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 Application of Functional Data Analysis to Identify Patterns of Malaria Incidence, to Guide Targeted Control Strategies

2020 ◽  
Vol 17 (11) ◽  
pp. 4168
Author(s):  
Sokhna Dieng ◽  
Pierre Michel ◽  
Abdoulaye Guindo ◽  
Kankoe Sallah ◽  
El-Hadj Ba ◽  
...  
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Temporal Dynamics ◽  
Malaria Incidence ◽  
Control Strategies ◽  
Control Measures ◽  
Smooth Functions ◽  
Validity Indices ◽  
Low Incidence

We introduce an approach based on functional data analysis to identify patterns of malaria incidence to guide effective targeting of malaria control in a seasonal transmission area. Using functional data method, a smooth function (functional data or curve) was fitted from the time series of observed malaria incidence for each of 575 villages in west-central Senegal from 2008 to 2012. These 575 smooth functions were classified using hierarchical clustering (Ward’s method), and several different dissimilarity measures. Validity indices were used to determine the number of distinct temporal patterns of malaria incidence. Epidemiological indicators characterizing the resulting malaria incidence patterns were determined from the velocity and acceleration of their incidences over time. We identified three distinct patterns of malaria incidence: high-, intermediate-, and low-incidence patterns in respectively 2% (12/575), 17% (97/575), and 81% (466/575) of villages. Epidemiological indicators characterizing the fluctuations in malaria incidence showed that seasonal outbreaks started later, and ended earlier, in the low-incidence pattern. Functional data analysis can be used to identify patterns of malaria incidence, by considering their temporal dynamics. Epidemiological indicators derived from their velocities and accelerations, may guide to target control measures according to patterns.

Approximation properties of repeated de la Vallée-Poussin means for piecewise smooth functions

2017 ◽  
Vol 60 (3) ◽  
pp. 695-713
Author(s):  
I. I. Sharapudinov ◽  
T. I. Sharapudinov ◽  
M. G. Magomed-Kasumov
Keyword(s):  
Piecewise Smooth ◽  
Approximation Properties ◽  
Smooth Functions ◽  
Piecewise Smooth Functions
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