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Table 1 Areas of application and the functional data analysis (FDA) features used in the 84 peer-review papers reporting application of FDA

From: Applications of functional data analysis: A systematic review

Year

Field of study

Outcome of interest

FDA features

Reference

Smoothing

Data reduction

Clustering

FLM

Forecasting

2010

Biomechanics

Walking velocity on force platform

-

-

-

FRM

-

[36]

Biomechanics

Kinematic gait data

Polynomial spline

FPCA

-

-

-

[37]

Biomedicine

Diffusion tensor imaging fiber images

Kernel

-

-

FRM

-

[38]

Biomedicine

Gene expression microarray data

Local polynomial

FPCA

FEM

-

-

[39]

Biomedicine

Spinal cord dorsal horn neurons

Locally weighted regression (LOESS)

-

K-Means

-

-

[40]

Demography

Age-specific mortality rates

Kernel

FPCA

-

-

-

[41]

Environment

Gas emissions

Kernel

-

-

-

-

[42]

Geophysics

Magnetometer

Kernel

FPCA

-

FRM

-

[43]

Medicine

Human growth

-

FPCA

-

-

-

[44]

Medicine

Age-specific breast cancer mortality rates

Penalized regression spline

FPCA

-

-

State space model

[45]

Medicine

Age-specific fall injury incidence rates

Penalized regression spline

FPCA

-

-

State space model

[23]

Medicine

Human vision

Wavelet

-

-

FANOVA

-

[46]

2009

Biology

Temporal fertility trajectories of medfly

-

FPCA

-

FMANOVA

-

[47]

Biomechanics

Kinematic gait data

-

-

-

FRM

-

[48]

Biomedicine

3-Tesla magnetic resonance imaging data

-

FPCA

-

-

-

[49]

Biomedicine

Denaturing gradient gel electrophoresis data

B-spline

FPCA

HCA

-

-

[50]

Biomedicine

microRNA transfection time-series microarray expression images

B-spline

FPCA

-

-

-

[51]

Biomedicine

Paediatric diffusion tensor imaging images

B-spline

FPCA

-

-

-

[52]

Biomedicine

Positron emission tomography time course data

Local polynomial

FPCA

-

-

-

[53]

Meteorology

Clickstream web data (Hurricane Katrina)

B-spline

-

-

FANOVA

-

[54]

2008

Biomechanics

Ankle dorsiflexion, knee flexion, Achilles tendon, calcaneal and leg abduction angles

Roughness penalty

FPCA

-

-

-

[55]

Biomedicine

Colon carcinogenesis experiments

Regression splines

FPCA

-

-

-

[56]

Biomedicine

Diffusion tensor imaging fiber images

B-spline

FPCA

-

-

-

[52]

Biomedicine

Temporal gene expression profiles for the Drosophila life cycle

Smoothing spline

FPCA

-

FRM

-

[57]

Biomedicine

Time-course gene expression data

B-spline

-

SVM

-

-

[58]

Biomedicine

Time-course gene expression data

B-spline

FPCA

LDA, QDA KNN, SVM

-

-

[59]

Demography

Mortality, fertility and migration rates

Weighted penalized regression spline

FPCA

-

-

State space model

[60]

Ecology

Plankton monitoring data

Roughness penalty

FPCA

-

-

-

[61]

Environment

Diurnal ozone and NOx cycles for transportation emission control

Fourier

FPCA

HCA

-

-

[62]

Finance

Cash flow and transactions

Wavelet

FPCA

-

-

FAR

[63]

Finance

Price formation and online auctions

Polynomial spline

-

-

FRM

-

[64]

Linguistics

Speech production variability in fricatives of children and adults

B-spline

FPCA

-

-

-

[65]

Meteorology

Plasma biomarkers

Kernel

-

-

FRM

-

[66]

Psychology

Emotional responses of musical listeners

Cubic B-spline

-

-

FANOVA

-

[67]

2007

Biology

Time-course gene expression yeast cell cycle

B-spline

FPCA

MBC

-

-

[68]

Biomedicine

MRI images

B-spline

-

-

-

-

[69]

Demography

Mortality and fertility rate

Penalized regression spline

FPCA

-

-

State space model

[25]

Engineering

Radar waveforms

Kernel

-

HCA

-

-

[70]

Environment

Diurnal ozone/NOx cycles and transportation emissions

Fourier

-

-

FANOVA

-

[71]

Environment

Stratospheric ozone levels

Cubic spline

FPCA

-

-

-

[72]

Medicine

Age-specific breast cancer mortality rates

Weighted local quadratic

FPCA

-

-

State space model

[24]

Medicine

Women urinary hormone profiles at midlife

Cubic spline

FPCA

-

-

-

[73]

Medicine

Haemoglobin levels in renal anaemia

B-spline

-

-

-

-

[74]

Neurology

Joint coordination data in motor development

B-spline

FPCA

-

-

-

[75]

2006

Biology

Time-course gene expression yeast cell cycle

B-spline

FPCA

FLR

-

-

[76]

Behavioural

Male medfly calling behaviour

-

FPCA

-

-

-

[77]

Biomechanics

Kinematic gait data (knee flexion angle)

Cubic B-spline

FPCA

LDA

-

-

[78]

Biomechanics

Knee joint kinematics in the vertical jump

B-spline

FPCA

-

-

-

[79]

Biomechanics

Kinematic gait data (sit to stand movements)

B-spline

-

-

-

-

[80]

Ecology

Water quality trend data (nutrient and sediment)

Fourier

FPCA

HCA

FRM

-

[81]

IT

Software complexity measure

Smoothing spline

-

-

-

-

[82]

Linguistics

Tongue tip velocity

B-spline

-

-

-

-

[83]

Physiology

Blood lactate for running speed on a treadmill

Polynomial spline

FPCA

-

-

-

[84]

Psychology

Tension judgement in music

B-spline

-

-

-

-

[85]

2005

Biology

Protein expression profiles

P-spline

FPCA

HCA

-

-

[86]

Biomechanics

Joint angles describing the limb motion

Regression spline

FPCA

-

-

-

[87]

Biomedicine

Functional magnetic resonance imaging data from 1.5-Tesla Magnetom vision

B-spline

FPCA

-

-

-

[88]

Biomedicine

Functional magnetic resonance imaging data from 3.0 T Allegra system-

B-spline

FPCA

-

-

-

[89]

Ecology

Smith McIntyre grab species

-

FPCA

HCA

-

-

[90]

Education

Trends in Mathematics and Science Achievement (TIMSS) score

Nonparametric spline

FPCA

CART,KNN

-

-

[91]

Finance

Cash flows in point of sale and ATM networks

Fourier

-

-

FANOVA

-

[92]

Linguistics

Speech movement records

Wavelets

-

-

-

-

[93]

Psychology

Tension judgement in music

B-spline

-

-

-

-

[94]

2004

Chemistry

Molecular weight distributions

B-spline

-

-

FRM

-

[95]

 

Medicine

Esophageal bolus flow

-

-

-

-

-

[96]

 

Meteorology

Biomarkers

Cubic spline

FPCA

-

-

-

[97]

 

Neurology

Automated atlas-based head size normalization

-

-

-

-

-

[98]

 

Psychology

Musical emotions and tension

B-spline

-

-

-

-

[99]

2003

Biomechanics

Digitized images of hand drawing curves generated by subjects treated with various facial preparation

Fourier

FPCA

-

FANOVA

-

[100]

Biomedicine

Longitudinal plasma folate data

Weighted local polynomial spline

FPCA

-

-

-

[101]

2002

Agriculture

Lodging score for rice fields based on a digital overhead image

Fourier

-

-

FRM

-

[102]

Biomedicine

Myocardial contractile function images

Cubic B-spline

FPCA

-

-

-

[103]

Economics

Monthly nondurable goods production index

B-spline

-

-

-

-

[104]

Medicine

Foetal heart rate data

Fourier

-

-

FRM

-

[18]

Medicine

Foetal heart rate data

Fourier

-

-

FLRM

-

[19]

2001

Satellite

Radar electromagnetic signals

Kernel

FPCA

-

 

-

[105]

2000

Biomechanics

Handwriting in Chinese

B-spline

FPCA

EDO

-

-

[14]

Linguistics

Harmonics-to-noise ratio of voice signals

B-spline

-

-

-

-

[106]

Meteorology

Annual cycle of sea surface temperatures

Polynomial spline

-

-

-

FAR

[107]

1999

Linguistics

Harmonics-to-noise ratio of voice signals

-

-

-

-

-

[108]

1998

Ecology

Abundance of the gray-sided vole Clethrionomys rufocanus

Log-spline

FPCA

-

-

-

[109]

1996

Linguistics

Vocal tract lip motion during speech

Smoothing spline

FPCA

-

FANOVA

-

[110]

1995

Biomechanics

Records of the force exerted by pinching a force meter with the tips of the thumb and forefinger an opposite sides

-

FPCA

-

-

-

[111]

 

Economics

Income distribution

-

FPCA

-

-

-

[112]

  1. FPCA - Functional principal component analysis; FEM - Functional embedding; HCA - Hierarchical cluster analysis; SVM - Support vector machine; LDA- Linear discriminant analysis; QDA - Quadratic discriminant analysis; KNN- K-nearest neighbours; MBC - Model based clustering; CART - Classification and regression tree; EDO - Estimated differential operators; FLM - Functional linear model; FRM - Functional linear regression model; FANOVA - Functional ANOVA; FMANOVA - Functional MANOVA; FFT - Functional F test; FLRM - Functional logistic regression model; FAR - Functional auto regressive model.