Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study

Febrero–Bande, Manuel; Galeano, Pedro; González–Manteiga, Wenceslao

doi:10.1111/insr.12116

Cited by 71 publications

(43 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the latter case, the principal component method reaches the same level of error as the conjugate gradient method only when m = 10 or more. These findings agree with the theoretical result of Proposition 2 and also with conclusions of Delaigle and Hall (2012a) and Febrero-Bande et al (2017) who point out that principal components need more degrees of freedom than partial least squares to reach good performance. In this regard ridge regularization seems to be between the two subspace methodologies.…”

Section: Behaviour Of Regularized Classifiers On Complete Datasupporting

confidence: 92%

Classification of functional fragments by regularized linear classifiers with domain selection

Kraus

Stefanucci

2018

Biometrika

View full text Add to dashboard Cite

We consider the problem of classification of functional data into two groups by linear classifiers based on one-dimensional projections of functions. We reformulate the task to find the best classifier as an optimization problem and solve it by regularization techniques, namely the conjugate gradient method with early stopping, the principal component method and the ridge method. We study the empirical version with finite training samples consisting of incomplete functions observed on different subsets of the domain and show that the optimal, possibly zero, misclassification probability can be achieved in the limit along a possibly nonconvergent empirical regularization path. Being able to work with fragmentary training data we propose a domain extension and selection procedure that finds the best domain beyond the common observation domain of all curves. In a simulation study we compare the different regularization methods and investigate the performance of domain selection. Our methodology is illustrated on a medical data set, where we observe a substantial improvement of classification accuracy due to domain extension.We consider the problem of classification of a functional observation into one of two groups. Classification of functional data is a rich, long-standing topic comprehensively overviewed in Baíllo et al. (2011b). It was recently shown by Delaigle and Hall (2012a) that depending on the relative geometric position of the difference of the group means, representing the signal, and covariance operator, summarizing the structure of the noise, certain classifiers can have zero misclassification probability. This remarkable phenomenon, called perfect classification, is a special property of the infinite-dimensional setting and cannot occur in the multivariate context, unless in degenerate cases. It was demonstrated by Delaigle and Hall (2012a) that a particularly simple class of linear classifiers, based on a carefully chosen one-dimensional projection of the function to

show abstract

Section: Behaviour Of Regularized Classifiers On Complete Datasupporting

confidence: 92%

Classification of functional fragments by regularized linear classifiers with domain selection

Kraus

Stefanucci

2018

Biometrika

View full text Add to dashboard Cite

show abstract

“…We follow the standard theoretical framework in FDA, which assumes that functions are realvalued and belong to a Hilbert space containing square-integrable functions over the observed range of wavelengths (Febrero-Bande et al, 2017;Reiss et al, 2017).…”

Section: Spectra As Functional Datamentioning

confidence: 99%

Functional data analysis techniques to improve the generalizability of near-infrared spectral data for monitoring mosquito populations

Esperança

Lambert

et al. 2020

Preprint

View full text Add to dashboard Cite

Near infrared spectroscopy is increasingly being used as an economical method to monitor mosquito vector populations in support of disease control. Despite this rise in popularity, strong geographical variation in spectra has proven an issue for generalising predictions from one location to another. Here, we use a functional data analysis approach-which models spectra as smooth curves rather than as a discrete set of points-to develop a method that is robust to geographic heterogeneity. Specifically, we use a penalised generalised linear modelling framework which includes efficient functional representation of spectra, spectral smoothing and regularisation. To ensure better generalisation of model predictions from one training set to another, we use cross-validation procedures favouring smoother representation of spectra. To illustrate the performance of our approach, we collected spectra for field-caught specimens of Anopheles gambiae complex mosquitoes -the most epidemiologically important vector species on the planet -in two sites in Burkina Faso. Using these spectra, we show how models trained on data from one site can successfully classify morphologically identical sibling species in another site, over 250km away. Whilst we apply our framework to species prediction, our unified statistical framework can, alternatively, handle regression analysis (for example, to determine mosquito age) and other types of multinomial classification (for example, to determine infection status). To make our methods readily available for field entomologists, we have created an open-source R package mlevcm. All data used is publicly also available.

show abstract

“…can only be defined on the Reproducing Kernel Hilbert space (RKHS) R 1/2 0 (H) of ε n , n ∈ Z (see Bosq, 2000; Da Prato and Zabczyk, 2002, Chapter 1, pp. [12][13][14][15][16].…”

Section: Remarkmentioning

confidence: 99%

Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors

Ruiz-Medina

Miranda

Espejo

2018

TEST

View full text Add to dashboard Cite

A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic normality and strong consistency is obtained, under suitable conditions. The correlation analysis is based on a componentwise estimator of the residual autocorrelation operator. When the dependence structure of the functional error term is unknown, a plug-in generalized least-squared regression parameter estimator is formulated. Its strong-consistency is proved as well. A simulation study is undertaken to illustrate the performance of the presented approach, under different regularity conditions. An application to financial panel data is also considered.Keywords ARH(1) errors · dynamical functional multiple regression · firm leverage maps · generalized least squared estimator · kernel regressors Mathematics Subject Classification (2010) MSC code1 60G25 · 60G60 and 62J05 · MSC code2 62J10

show abstract

Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study

Cited by 71 publications

References 38 publications

Classification of functional fragments by regularized linear classifiers with domain selection

Classification of functional fragments by regularized linear classifiers with domain selection

Functional data analysis techniques to improve the generalizability of near-infrared spectral data for monitoring mosquito populations

Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors

Contact Info

Product

Resources

About