Variation pattern classification of functional data

نویسندگان

چکیده

A new classification method for functional data is proposed in this article. This work motivated by the need to identify features that discriminate between neurological conditions on which local field potentials (LFPs) were recorded. Regardless of condition, these LFPs have zero mean, and thus first moments random processes do not discriminating power. We propose variation pattern (VPC) employs second-moment structure as feature uses Hilbert–Schmidt norm measure discrepancy different groups. The VPC demonstrated be sensitive discrepancy, potentially leading a higher rate classification. One important innovation lies dimension reduction where adaptively determines basis functions (discriminative functions) account major discrepancy. In addition, selected discriminative provide insights into groups because they reveal differentiate Consistency properties are established and, furthermore, simulation studies analysis rat brain LFP trajectories empirically demonstrate advantages effectiveness method. Le présent article une nouvelle méthode de données fonctionnelles. Il est motivé par la nécessité d'identifier les caractéristiques capables différencier entre neurologiques sous lesquelles des potentiels champ ont été enregistrés. Indépendamment condition neurologique, ces possèdent moyenne nulle, ce qui prive premiers processus aléatoires tout pouvoir discriminant. Les auteurs proposent profils utilise du second moment comme caractéristique discriminante et applique norme Hilbert-Schmidt pour mesurer l'écart structures au sein différents groupes. s'avère que cette sensible aux écarts peut, conséquent, donner lieu à un taux plus élevé. Une importante approche réside dans réduction car fonctions base (fonctions discriminantes) expliquent majeur sont déterminées manière adaptative. En outre, discriminantes sélectionnées fournissent aperçus sur groupes parce qu'elles révèlent différencient d'établir quelques propriétés convergence proposée, illustrent ses avantages son efficacité en ayant recours simulations l'analyse trajectoires le cerveau rats. It clinicians able rapidly detect stroke onset order minimize debilitating downstream effects stroke. Early detection gives patients best possible prognosis quick recovery minimal damage. By contrast, late associated with poor including longer times, nonrecovery from profound motor function, speech, memory. article, we examine recorded rats during an experiment. To develop statistical discrimination prestroke poststroke signals. setting, there training available, known group labels (pre vs. onset). goal here separate two classes signals unknown (normal abnormal or particular). envision developing can track online purpose providing some warning when start exhibit features. main contribution classifier based (lagged) operator under setting similar mean functions. does rely any distributional assumption, procedure has broad potential applicability. noted accuracy influenced factors, background noise curve classified. often case that, more used groups, typically becomes pronounced. However, variability uncertainty also increases. Therefore, it necessarily advantageous incorporate many discriminant analysis—if employed low power classes. As advantage, selects attenuates nuisance effect past decades, variety methods been proposed. James & Hastie (2001), Preda, Saporta Lévéder (2007), Shin (2008), Delaigle Hall (2012) studied linear analysis. Biau, Bunea Wegkamp (2005) Fromont Tuleau (2006) k -nearest neighbour Müller Stadtmüller generalized models, Leng (2006), Li Ghosal (2018) multinomial logistic models multiclass Glendinning Herbert (2003), Chiou Song al. (2008) principal component classifiers. (2013) Dai, Yao (2017) Bayesian quadratic classifier. Tian interpretable technique Some carefully selection problem. Saito Coifman (1995, 1996) select wavelet packets extract information problems. Wang, Ray Mallick (2007) Fryzlewicz Ombao (2009) methods. Huang, Stoffer (2004) Ho procedures nonstationary time series. novelty works bases SLEX library illuminate difference processes. Böhm (2010) multivariate research classification, such (2004), (2009), (2013), (2017). methods, covariance operator/matrix accounted fixed group-wise components, capture difference. Compared existing following advantages: (1) entirely driven nonparametric, making applicable range robust model misspecification. (2) selects, adaptive manner, sequence orthonormal accounts most operators. Thus, improve ability (3) takes intra-curve information, provides (4) framework applied both independent dependent rest organized follows. Section 2 presents displays theoretical result performs asymptotically perfectly regularity conditions. 3, study finite-sample simulations. 4, implemented classify epochs. Conclusions made 5. Technical proofs additional real phoneme found Supplementary Material. relevant code GitHub at https://github.com/DrJiaoSH/VPC. Let { X ( t ) : ∈ ℕ , [ 0 1 ] } set realizations elements Hilbert space L ], inner product defined ⟨ x y ⟩ = ∫ d t, ‖ t. Assume E < ∞, define function μ C · →

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ژورنال

عنوان ژورنال: Canadian journal of statistics

سال: 2022

ISSN: ['0319-5724', '1708-945X']

DOI: https://doi.org/10.1002/cjs.11738