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- W2970523552 abstract "Functional Data Analysis (FDA) provides informationabout curves that vary over a continuum. In this thesis, we proposetwo novel methodologies to classify a functional dataset, usingsupervised learning. The first methodology is based on NearestNeighbours methods for functional data and classifies based onranks of the functional signed depth. The proposed classifier usesthe simplicity of the k-Ranked Nearest Neighbours (k-RNN) and itspractical efficiency, exploiting the fact that the k-RNN providesconditional probabilities where the depth of an observed curvebelongs to a particular group. Using this, we develop aprobabilistic classifier and construct point-wise confidenceintervals using a bootstrap approach. Following a generalizedadditive model, we propose a classifier based on the signed depthand the distance to the mode for functional observations. By meansof a simulation study, we compare the performance of the proposedclassifier against other nearest neighbours and depth classifiers.We also investigate the performance of the proposed classifierunder different types of outliers common to these kinds ofproblems; we see that our proposed method works well under thesedifferent scenarios. The second methodology we developed is basedon log ratios of density estimates using Bayes’ theorem. Wepropose a nonparametric adaptive density Bayesian classifier basedon log ratios density estimates of functional principal componentscores combined with different semimetrics. We study some of themain properties of the density estimator in a finite dimensionalspace and conduct a simulation study to investigate the performanceof the proposed classifier under two semimetrics: the semimetricbased on principal components scores and the semimetric based onpartial least squares. We also compare the performance of theproposed classifier against different methods for simulated andreal datasets. Imbalanced sample sizes appear frequently in theclassification problem and present multiple issues. We propose amethod to strengthen observations that are at the boundary. Westudy different sampling methods to strengthen observations thatare more susceptible to misclassification and we generate newcurves by considering a linear combination of the observations inthe border and the observations closes in depth." @default.
- W2970523552 created "2019-09-05" @default.
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- W2970523552 date "2019-01-01" @default.
- W2970523552 modified "2023-09-27" @default.
- W2970523552 title "Discriminant Anlaysis: A functionalperspective" @default.
- W2970523552 hasPublicationYear "2019" @default.
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