Application Of Functional Data Analysis Research Articles

Demonstrating the relevance of spatial-functional statistical analysis in marine ecological studies: The case of environmental variations in micronektonic layers

In this study, we conducted an analysis of a multifrequency acoustics dataset acquired from scientific echosounders in the West African water. Our objective was to explore the spatial arrangement of marine organism aggregations. We investigated various attributes of these intricate biological entities, such as thickness, relative density, and depth, in relation to their surroundings. These environmental conditions were represented at a fine scale using a towed multiparameter system. This study is closely intertwined with two key domains: Fisheries acoustics techniques and functional data analysis. Fisheries acoustics techniques facilitate the collection of high-resolution spatial and temporal data concerning marine organisms at various depths and spatial scales, all without causing any disturbance. On the other hand, spatial-functional data analysis is a statistical approach for examining data characterised by functional attributes distributed across a spatial domain. This analysis encompasses dimension reduction techniques, as well as supervised and unsupervised methods, which take into consideration spatial dependencies within extensive datasets.We began by applying multivariate statistical techniques and subsequently employed Functional Data Analysis (FDA). In the modeling section, we introduced the spatial dimension with the spatial coordinates as covariates in the General Additive Model (GAM) and Functional Generalized Spectral Additive Model (FGSAM) models, aiming to underscore its relevance in those contexts. In an exploratory phase, Multivariate Functional Principal Component Analysis provided detailed insights into the variations of parameters at different depths, a capability not offered by traditional Principal Component Analysis. When it came to regression tasks, we explored the interactions between descriptors of Sound Scattering Layers and key environmental variables, both with and without considering spatial dimensions. Our findings revealed significant distinctions between northern and southern Sound Scattering Layers, as well as between coastal and high-sea regions. The use of the spatial locations enhanced the performance of GAM and FGSAM, particularly in the case of salinity, reflecting the influence of water mixing and seawater temperature. The multifaceted effects of environmental variations on Sound Scattering Layers underscore the importance of spatial-functional statistical analysis in ecological studies involving complex, spatially functional objects. Beyond the scope of this specific case study, the application of functional data analysis shows promise for a wide array of ecological studies dealing with extensive spatial datasets.

Rapid Material Characterization using Smart Skin with functional Data Analysis

Automotive industries in the last decade are demanding for lightweight, corrosion resistance and improved fatigue performance materials. Composites having all such properties quickly gain popularity. Due to complex fabrication methods, composites are known for various process defects. Thus, monitoring and characterizing the composite component before assembly is necessary to maintain the overall structural integrity. Further a rapid and reliable inspection is much needed addition in most automotive industries to save time.
 Non-Destructive Evaluation (NDE) is popular for component testing in the automobile industry because they do not cause any permanent alteration to components. Some NDE techniques require sensors (Piezo Electric transducers, PVDF films, Optical fiber, etc.) that need to be bonded to the structure for testing. Some of these sensors are expensive and cannot be reused once detached. This work aims at the reusability of sensors. Further, the reusable sensors can be deployed in an array configuration for multi-purpose NDE. SMART Skin shall be explained as a Multiple-Transmitter-Multiple-Receiver (MTMR) Piezo-ceramic based sensor (PZT) array which is embedded to a conformable skin. The bottom layer of the skin is coated with pressure-sensitive adhesive to be attached to most curved and non-curved structural surfaces. Each PZT sensor nodes are individually controlled by a MATLAB code that actuates and receive the GW waves signals.
 In this work, we have validated the ability of rapid material characterization using isotropic materials.
 Using experimental data collected by the proposed methodology, we have developed an automated material classification algorithm using various machine learning algorithms. A novel application of functional data analysis (fDA) which converts discrete samples into continuous curves is used. The curves are represented as linear combinations of basis functions. The advantage of this fDA method is that we use the shape of the signal instead of extracting features from the signal. Several choices of basis coefficients such as fourier series, wavelet and B-spline are considered of which spline basis gives the best results. These basis coefficients are then feed into machine learning models like Support Vector Machine (SVM), Random Forest (RF), k nearest neighbor (knn) for classification. The efficacy of this novel method is compared with conventional feature extraction techniques such as zero-crossing coefficients, absolute maximum value, different statistical features like mean and variance, energy of the signal. Encouraging results are obtained that shows the fDA methodology is efficient over the conventional feature extraction methods as it improves the prediction performance on the classifier and result in a faster and cost-effective model by reducing the predictor dimensionality.

Regional and temporal patterns of influenza: Application of functional data analysis

BackgroundThe accurate estimation of temporal patterns of influenza may help in utilizing hospital resources and guiding influenza surveillance. This paper proposes functional data analysis (FDA) to improve the prediction of temporal patterns of influenza.MethodsWe illustrate FDA methods using the weekly Influenza-like Illness (ILI) activity level data from the U.S. We propose to use the Fourier basis function for transforming discrete weekly data to the smoothed functional ILI activities. Functional analysis of variance (FANOVA) is used to examine the regional differences in temporal patterns and the impact of state's political orientation.ResultsThe ILI activity has a very distinct peak at the beginning and end of the year. There are significant differences in average level of ILI activities among geographic regions. However, the temporal patterns in terms of the peak and flat time are quite consistent across regions. The geographic and temporal patterns of ILI activities also depend on the political make-up of states. The states affiliated with Republicans had higher ILI activities than those affiliated with Democrats across the whole year. The influence of political party affiliation on temporal pattern is quite different among geographic regions.ConclusionsFunctional data analysis can help us to reveal the temporal variability in average ILI levels, rate of change in ILI levels, and the effect of geographical regions. Consideration should be given to wider application of FDA to generate more accurate estimates in public health and biomedical research.

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

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.

Application of Functional Data Analysis for the Prediction of Maximum Heart Rate

Maximum heart rate (MHR) is widely used in the prescription and monitoring of exercise intensity, and also as a criterion for the termination of sub-maximal aerobic fitness tests in clinical populations. Traditionally, MHR is predicted from an age-based formula, usually 220-age. These formulae, however, are prone to high predictive errors that potentially could lead to inaccurately prescribed or quantified training or inappropriate fitness test termination. In this paper, we used functional data analysis (FDA) to create a new method to predict MHR. It uses heart rate data gathered every 5 seconds during a low intensity, sub-maximal exercise test. FDA allows the use of all the information recorded by monitoring devices in the form of a function, reducing the amount of information needed to generalize a model, besides minimizing the curse of dimensionality. The functional data model created reduced the predictive error by more than 50% compared to current models within the literature. This new approach has important benefits to clinicians and practitioners when using MHR to test fitness or prescribe exercise.

Global Sensitivity Analysis of Transient Code Output Applied to a Reflood Experiment Model Using the TRACE Code

Appropriate model assessment requires proper understanding of the impact of variations of model parameters and their interactions on results. However, in many thermal-hydraulic (TH) simulations, the code often predicts time-dependent output where the impact of model parameter variations on the overall transient is not easily discernible from quantities of interest (QoIs) based on the maximum, minimum, or average over space and/or time. This work proposes a methodology to analyze transient code output in a more comprehensive manner and coupled with established global sensitivity analysis (SA) methods.This paper first describes how the particularities of transient output variations can be characterized through application of functional data analysis (FDA) techniques. The convoluted amplitude and phase variations in the output are separated first by using a registration technique. The high-dimensional transient output is then projected in reduced dimension by using principal component analysis. Based on this, innovative QoIs that capture the variation over the whole course of the transient are finally derived.The subsequent global SA is a two-step process. First, the noninfluential parameters are identified using the efficient Morris screening method. The exclusion of these parameters reduces the size of the problem and decreases the cost of the downstream analysis. Second, the sensitivity of the influential model parameters with respect to a selected QoI is computed using the Sobol’ method. The method gives a set of sensitivity indices quantifying the contributions of input variations to the QoI variation considering possible interactions among the parameters.The applicability of the proposed methodology is demonstrated by analyzing a 26-parameter reflood experiment simulation model with the TRAC/RELAP Computational Engine (TRACE) TH system code. The FDA-derived QoI on the time-dependent cladding temperature was able to give a deeper insight on particular modes of variations exhibited by the model over the whole course of the reflood transient. That is, the variations in the cladding temperature transient could be simply divided into two modes: the reversal phase (from heatup until shortly after the temperature turnaround) and the descent phase (onward until quenching). The applied SA method was then able to attribute the variation of these two modes to the variation of the model parameters. It was found that the model was additive during the temperature reversal phase with dispersed flow film boiling—related parameters contributing to most of the model output variation, consistent with the adopted phenomenological model. Yet, the variation during the temperature descent could only be explained through parameter interactions indicating a more complex input/output relationship.Through study of this particular case, it is shown that if different QoIs based on the same time-dependent output variable are used—thus inspecting functional aspects of the output—the model might behave differently, being additive with respect to one QoI and interacting with respect to another, thus revealing more information on the model behavior, which might be overlooked in a SA based on extreme or time-averaged QoIs.

Application of functional data analysis in classification and clustering of functional near-infrared spectroscopy signal in response to noxious stimuli.

We introduce the application of functional data analysis (fDA) on functional near-infrared spectroscopy (fNIRS) signals for the development of an accurate and clinically practical assessment method of pain perception. We used the cold pressor test to induce different levels of pain in healthy subjects while the fNIRS signal was recorded from the frontal regions of the brain. We applied fDA on the collected fNIRS data to convert discrete samples into continuous curves. This method enabled us to represent the curves as a linear combination of basis functions. We utilized bases coefficients as features that represent the shape of the signals (as opposed to extracting defined features from signal) and used them to train a support vector machine to classify the signals based on the level of induced pain. We achieved 94% of accuracy to classify low-pain and high-pain signals. Moreover applying hierarchical clustering on the coefficients, we found three clusters in the data which represented low-pain (one cluster) and high-pain groups (two clusters) with an accuracy of 91.2%. The center of these clusters can represent the prototype fNIRS response of that pain level.

Functional unfold principal component regression methodology for analysis of industrial batch process data

This work proposes a methodology utilizing functional unfold principal component regression (FUPCR), for application to industrial batch process data as a process modeling and optimization tool. The methodology is applied to an industrial fermentation dataset, containing 30 batches of a production process operating at Novozymes A/S. Following the FUPCR methodology, the final product concentration could be predicted with an average prediction error of 7.4%. Multiple iterations of preprocessing were applied by implementing the methodology to identify the best data handling methods for the model. It is shown that application of functional data analysis and the choice of variance scaling method have the greatest impact on the prediction accuracy. Considering the vast amount of batch process data continuously generated in industry, this methodology can potentially contribute as a tool to identify desirable process operating conditions from complex industrial datasets. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1986–1994, 2016

Review and application of functional data analysis to chemical data—The example of the comparison, classification, and database search of forensic ink chromatograms

Functional data analysis is a relatively recent statistical method that can be applied to any dataset that can be thought of as a function. Functional data analysis considers functions as random elements. Modern chromatographic or spectroscopic techniques typically record analytical outputs as a function of time or wavelength. The purpose of this paper is to investigate the potential of functional data analysis for the characterization, comparison, and classification of chemical data. Forensic examination of ink is used as the main example in this paper as it covers different aspects of functional data analysis: (a) thin-layer chromatograms resulting from analysis of ink samples are characterized as functions of time and wavelength; (b) multiple samples analyzed at different times, or by different analysts, are registered into a common space; (c) a dimension reduction technique is applied to the sample functions to enable (d) their use for comparing between ink samples and for clustering large databases of inks. Our algorithms showed excellent performance and can readily be implemented to search and retrieve chemical profiles in large databases. From a theoretical standpoint, functional data analysis allows for a natural extension of multivariate analysis to datasets that can be thought of as functions. Algorithmically, functional data analysis proves to be a powerful technique that enables to detect functions minima and maxima, register multiple functions to a common space, and control the dimensionality and smoothness of a functional dataset. Nevertheless, we found that the implementation of functional data analysis is computationally complex when compared to classic multivariate analysis.

Wavelet‐Based Clustering for Mixed‐Effects Functional Models in High Dimension

We propose a method for high-dimensional curve clustering in the presence of interindividual variability. Curve clustering has longly been studied especially using splines to account for functional random effects. However, splines are not appropriate when dealing with high-dimensional data and can not be used to model irregular curves such as peak-like data. Our method is based on a wavelet decomposition of the signal for both fixed and random effects. We propose an efficient dimension reduction step based on wavelet thresholding adapted to multiple curves and using an appropriate structure for the random effect variance, we ensure that both fixed and random effects lie in the same functional space even when dealing with irregular functions that belong to Besov spaces. In the wavelet domain our model resumes to a linear mixed-effects model that can be used for a model-based clustering algorithm and for which we develop an EM-algorithm for maximum likelihood estimation. The properties of the overall procedure are validated by an extensive simulation study. Then, we illustrate our method on mass spectrometry data and we propose an original application of functional data analysis on microarray comparative genomic hybridization (CGH) data. Our procedure is available through the R package curvclust which is the first publicly available package that performs curve clustering with random effects in the high dimensional framework (available on the CRAN).

Application of functional data analysis to investigate seasonal progression with interannual variability in plankton abundance in the Bay of Fundy, Canada

The statistical technique of functional data analysis (FDA) is applied to a time series analysis of plankton monitoring data. The analysis is focused on revealing patterns in the seasonal cycle to assess interannual variability of several different taxonomic groups of plankton. Cell concentrations of diatom, dinoflagellate and zooplankton abundances from the Bay of Fundy, Canada provide the observations for analysis. FDA was performed on the log-transformed abundance data as a new approach for treating such types of sparse and noisy data. Differences in the seasonal progression were seen, with peak numbers, timings and abundance levels varying for the three groups as determined by curve registration and higher order derivatives using the objectively fit FDA curves. Nonmetric multidimensional scaling was used to capture seasonal variation among years. These results were further assessed in terms of dominant species and the relationships between groups for different seasons and years. It is anticipated that the easy to use, general and flexible technique of FDA could be applied to a wide variety of marine ecological data that are characterized by missing values and non-Gaussian distributions.

Three-Dimensional Transoesophageal Echocardiography is Superior to Conventional Mitral Valve Mapping for Location of Valve Pathology

Purpose: Ventricular function is typically measured at specific moments during the cardiac cycle. However cardiac motion is a continuum with close interrelationships between systolic and diastolic phases. Real-time threedimensional echocardiography (RT3DE) calculates 3D left ventricular volumes (3DLVV) for each frame of an imaging sequence. Converting the repeated volume measurements to a continuous function of time allows application of functional data analysis techniques.We explore the feasibility of estimating total cardiac power from functional 3DLVV data, and describe its relationship with conventional 2D ejection fraction (2DEF). Method: Echocardiography was performed in 16 normal subjects and 12 patients post-acute coronary syndrome (ACS): Simpson’s biplane 2DEF and RT3DE loops (Philips iE33) were obtained. For each subject, 3DLVVs (proportional to end-diastolic volume) were converted to a function of time (R statistical software). The first and second derivatives were plotted, the area of which equates to energy. Power was estimated as energy divided by durat R u e l p C i m s m e

기온 강수량 자료의 함수적 데이터 분석

본 연구는 함수적 데이터 분석의 몇 가지 이론에 대해 소개하고 분석 기법을 실제 자료에 적용하는 내용을 다루었다. 함수적 데이터 분석의 이론적 내용으로 기저를 이용해 자료를 함수적 데이터로 표현하는 방법, 그리고 함수적 데이터의 변동성을 조사하는 주성분분석, 선형모형 등에 대해 살펴보았다. 그리고 우리나라 기온 데이터와 강수량 데이터를 대상으로 각각 함수적 데이터 분석 기법을 적용해 보았다. 또한, 기온과 강수량 데이터에 대해 함수적 회귀모형을 적합시켜 두 변수간의 함수관계를 살펴보았다. In this paper we review some methods for analyzing functional data and illustrate real application of functional data analysis. Representing methods for functional data by using basis function, analyzing functional variation by functional principal component analysis and functional linear models are reviewed. For a real application, we use temperature and precipitation data measured in Korea from the January of 1970 to the May of 2004. We apply functional principal component analysis for each data and test the significance of regional division done by using shining hours. We also estimate functional regression model for temperature and precipitation.

Opportunities and Challenges Applying Functional Data Analysis to the Study of Open Source Software Evolution

This paper explores the application of functional data analysis (FDA) as a means to study the dynamics of software evolution in the open source context. Several challenges in analyzing the data from software projects are discussed, an approach to overcoming those challenges is described, and preliminary results from the analysis of a sample of open source software (OSS) projects are provided. The results demonstrate the utility of FDA for uncovering and categorizing multiple distinct patterns of evolution in the complexity of OSS projects. These results are promising in that they demonstrate some patterns in which the complexity of software decreased as the software grew in size, a particularly novel result. The paper reports preliminary explorations of factors that may be associated with decreasing complexity patterns in these projects. The paper concludes by describing several next steps for this research project as well as some questions for which more sophisticated analytical techniques may be needed.

Functional data analysis of prosodic effects on articulatory timing

An application of functional data analysis (FDA) (Ramsay and Silverman, 2005, Functional Data Analysis, 2nd ed. (Springer-Verlag, New York)) for linguistic experimentation is explored. The functional time-registration method provided by FDA is shown to offer novel advantages in the investigation of articulatory timing. Traditionally, articulatory studies examining the effects of linguistic variables such as prosody on articulatory timing have relied on comparing the durations of speech intervals of interest defined by kinematic landmarks. Such measurements, however, do not preserve information on the detailed, continuous pattern of articulatory timing that unfolds during these intervals. We present an approach that allows the analysis of entire, continuous kinematic trajectories obtained in a movement tracking experiment examining the influence of a phrasal boundary on articulatory patterning. FDA time deformation functions, after alignment of test and reference (control) signals, reveal delaying of articulator movement (i.e., slowing of the internal clock rate) in the presence of a phrase boundary as the speech stream recedes from the boundary. This is a theoretically predicted pattern (Byrd and Saltzman, 2003, The elastic phrase: Modeling the dynamics of boundary-adjacent lengthening, Journal of Phonetics 31, 149-180.), which would be more difficult to validate with a traditional interval-based approach. It is concluded that the FDA time alignment method provides a useful tool for characterizing timing patterns in linguistic experimentation based on continuous kinematic trajectories.

Time normalization of voice signals using functional data analysis.

The harmonics-to-noise ratio (HNR) has been used to quantify the waveform irregularity of voice signals [Yumoto et al., J. Acoust. Soc. Am. 71, 1544-1550 (1982)]. This measure assumes that the signal consists of two components: a harmonic component, which is the common pattern that repeats from cycle-to-cycle, and an additive noise component, which produces the cycle-to-cycle irregularity. It has been shown [J. Qi, J. Acoust. Soc. Am. 92, 2569-2576 (1992)] that a valid computation of the HNR requires a nonlinear time normalization of the cycle wavelets to remove phase differences between them. This paper shows the application of functional data analysis to perform an optimal nonlinear normalization and compute the HNR of voice signals. Results obtained for the same signals using zero-padding, linear normalization, and dynamic programming algorithms are presented for comparison. Functional data analysis offers certain advantages over other approaches: it preserves meaningful features of signal shape, produces differentiable results, and allows flexibility in selecting the optimization criteria for the wavelet alignment. An extension of the technique for the time normalization of simultaneous voice signals (such as acoustic, EGG, and airflow signals) is also shown. The general purpose of this article is to illustrate the potential of functional data analysis as a powerful analytical tool for studying aspects of the voice production process.

Functional clustering algorithm for high-dimensional proteomics data.

Clustering proteomics data is a challenging problem for any traditional clustering algorithm. Usually, the number of samples is largely smaller than the number of protein peaks. The use of a clustering algorithm which does not take into consideration the number of features of variables (here the number of peaks) is needed. An innovative hierarchical clustering algorithm may be a good approach. We propose here a new dissimilarity measure for the hierarchical clustering combined with a functional data analysis. We present a specific application of functional data analysis (FDA) to a high-throughput proteomics study. The high performance of the proposed algorithm is compared to two popular dissimilarity measures in the clustering of normal and human T-cell leukemia virus type 1 (HTLV-1)-infected patients samples.