Supervised classification for functional data: A weighted distance approach

Alonso, Ana; Casado, David; Romo, Juan

doi:10.1016/j.csda.2012.01.013

Cited by 31 publications

(18 citation statements)

References 22 publications

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“…Li and Yu (2008) proposed to use F -statistics to select small subintervals in the domain and to restrict the analysis to those. Other techniques include the weighted distance method of Alonso et al (2012) and the componentwise approach of Delaigle et al (2012).…”

Section: Functional Datamentioning

confidence: 99%

Multivariate and functional classification using depth and distance

Hubert

Rousseeuw

Segaert

2016

Adv Data Anal Classif

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We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the data. For this purpose we can use the bagdistance which is based on halfspace depth. It satisfies most of the properties of a norm but is able to reflect asymmetry when the class is skewed. Alternatively we can compute a measure of outlyingness based on the skew-adjusted projection depth. In either case we propose the DistSpace transform which maps each data point to the vector of its distances to all classes, followed by k-nearest neighbor (kNN) classification of the transformed data points. This combines invariance and robustness with the simplicity and wide applicability of kNN. The proposal is compared with other methods in experiments with real and simulated data. arXiv:1504.01128v3 [stat.ME] 7 Jul 2016 z := λx + (1 − λ)y. We can verify that z := (λg(x) + (1 − λ)g(y)) −1 z is a convex combination of c x and c y . By compactness of B we know that c x , c y ∈ B, and from convexity of B it then follows that z ∈ B. Therefore c z = c z z so that finally g(z) = z c z z z = λg(x) + (1 − λ)g(y) .

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Section: Functional Datamentioning

confidence: 99%

Multivariate and functional classification using depth and distance

Hubert

Rousseeuw

Segaert

2016

Adv Data Anal Classif

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“…Ferraty and Vieu [23] showed that the concept of nearness in functional data analysis is adequately met by so-called semi-metrics in the space of the functional predictors. Alonso et al [24], for example, use a pre-defined semi-metric on derivatives of functional observations to generate multivariate data points that are then used as input in a classification algorithm. The idea of our nearest neighbor ensemble is not to use a single semi-metric, but a set of semi-metrics, where each semi-metric focuses on a certain feature of the curve.…”

Section: Introductionmentioning

confidence: 99%

Nearest neighbor ensembles for functional data with interpretable feature selection

Fuchs

Gertheiss

Tutz

2015

Chemometrics and Intelligent Laboratory Systems

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“…Many methods have been proposed to extract useful information from functional data (Ramsay and Silverman (2006), Ferraty and Vieu (2006), and Horváth and Kokoszka (2012)). Functional classification is an essential task in many applications, e.g., diagnosing diseases based on curves or images from medical test results, recognizing handwriting or speech patterns, and classifying products (Epifanio (2008), , Alonso et al (2012), Sguera et al (2014), and Galeano et al (2015)). Statistical depth was initially defined to rank multivariate data, mimicking the natural order of univariate data.…”

Section: Introductionmentioning

confidence: 99%

An Outlyingness Matrix for Multivariate Functional Data Classification

Dai¹,

Genton²

2018

STAT SINICA

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The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by extending directional outlyingness, an effective measure of the shape variation of curves that combines the direction of outlyingness with conventional statistical depth. We propose two classifiers based on directional outlyingness and the outlyingness matrix, respectively. Our classifiers provide better performance compared with existing depth-based classifiers when applied on both univariate and multivariate functional data from simulation studies. We also test our methods on two data problems: speech recognition and gesture classification, and obtain results that are consistent with the findings from the simulated data.

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Supervised classification for functional data: A weighted distance approach

Cited by 31 publications

References 22 publications

Multivariate and functional classification using depth and distance

Multivariate and functional classification using depth and distance

Nearest neighbor ensembles for functional data with interpretable feature selection

An Outlyingness Matrix for Multivariate Functional Data Classification

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