Multivariate and functional classification using depth and distance

Hubert, Mia; Rousseeuw, Peter J.; Segaert, Pieter

doi:10.1007/s11634-016-0269-3

Cited by 48 publications

(65 citation statements)

References 54 publications

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“…Therefore, from (16)- (17), and by the Kolmogorov, Marcinkiewicz and Zygmund strong law of large numbers (see, e.g., [18,Theorem 3.23]), we see that, whenever X ∈ L 4/3 , B ω,n − B ω,n 1 → 0 a.s.…”

Section: Appendixmentioning

confidence: 95%

New distance measures for classifying X-ray astronomy data into stellar classes

Baı́llo

Cárcamo

Getman

2018

Adv Data Anal Classif

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The classification of the X-ray sources into classes (such as extragalactic sources, background stars, . . . ) is an essential task in astronomy. Typically, one of the classes corresponds to extragalactic radiation, whose photon emission behaviour is well characterized by a homogeneous Poisson process. We propose to use normalized versions of the Wasserstein and Zolotarev distances to quantify the deviation of the distribution of photon interarrival times from the exponential class. Our main motivation is the analysis of a massive dataset from X-ray astronomy obtained by the Chandra Orion Ultradeep Project (COUP). This project yielded a large catalog of 1616 X-ray cosmic sources in the Orion Nebula region, with their series of photon arrival times and associated energies. We consider the plug-in estimators of these metrics, determine their asymptotic distributions, and illustrate their finite-sample performance with a Monte Carlo study. We estimate these metrics for each COUP source from three different classes. We conclude that our proposal provides a striking amount of information on the nature of the photon emitting sources. Further, these variables have the ability to identify X-ray sources wrongly catalogued before. As an appealing conclusion, we show that some sources, previously classified as extragalactic emissions, have a much higher probability of being young stars in Orion Nebula.An important initial step in the analysis of stellar populations is the classification of samples into different classes of sources (see [5]). The definition of the classes (foreground stars, background stars, different types of pre-main-sequence stars, etc.) depends on the research project, but it is always of interest to identify extragalactic sources (see [5]; [9]). Frequently, the allocation has a degree of uncertainty, to the extent that some of the astronomical sources might remain unclassified (see [11]) or even wrongly catalogued.X-ray astronomy deals with the detection and observation of astrophysical objects by means of the properties of their X-ray emissions. There are many astronomical sources of X-rays, such as galaxy clusters, black holes or different types of stars. In X-ray astronomy, classification of the data (that is, the X-ray sources) is accomplished using all the information provided by source features such as its location and X-ray and infrared properties (see [5]). As X-radiation is blocked by the atmosphere of Earth, cosmic X-ray emissions can only be detected by space telescopes. This article is motivated by a real dataset obtained as a result of Chandra Orion Ultradeep Project (COUP). It was fulfilled with one of the "Great Observatories" of NASA, the Chandra X-ray space telescope. Chandra was designed to observe X-ray emissions from high-energy regions of the space such as supernovas, black holes or star clusters as the Orion Nebula.In this work, we focus on a massive collection of X-ray astronomical sources derived from a 2003 exposure of Chandra to the Orion Nebula region ([12]). For each of the s...

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Section: Appendixmentioning

confidence: 95%

New distance measures for classifying X-ray astronomy data into stellar classes

Baı́llo

Cárcamo

Getman

2018

Adv Data Anal Classif

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“…Generally speaking, by a robust statistical procedure we mean a procedure which correctly expresses a tendency represented by an influential majority of probability mass, or a fraction of data (Hubert, Rousseeuw, Segaert, 2016). In the context of a classifier, we usually consider its robustness with respect to a contamination of a training sample.…”

Section: Robustness Of a Classification Rule For Functional Datamentioning

confidence: 99%

“…It should be stressed, that there is no agreement as to the breakdown point or influence function concepts even in the multivariate classification case, however some important results on influence functions were obtained by Christmann, Van Messem (2008) (see also Steinwart, Christmann, 2008). Some attempts to tackle the robustness issue in functional classification case have been made (for example, see Hubert, Rousseeuw, Segaert, 2016). We follow the qualitative robustness concept and adapt it to the functional classification case.…”

Section: Robustness Of a Classification Rule For Functional Datamentioning

confidence: 99%

“…Robust classification rule denotes a rule, which focuses on an influential majority of data and which copes with certain amount of problems with data. In multivariate case the concept of robustness in a context of classifiers was studied, among others, by Hubert, Rousseeuw, Segaert (2016), and Christmann, Salibian-Barrera, Van Aelst (2013). Hubert, Van Driessen (2004) considered an overall robustness of a classifier in terms of breakdown point for the worst class performance.…”

Section: Introductionmentioning

confidence: 99%

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A Critical Study of Usefulness of Selected Functional Classifiers in Economics

2020

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In this paper we conduct a critical analysis of the most popular functional classifiers. Moreover, we propose a new classifier for functional data. Some robustness properties of the functional classifiers are discussed as well. We can use an approach worked out in this paper to predict the expected state of the economy from aggregated Consumer Confidence Index (CCI, measuring consumers optimism) and Industrial Price Index (IPI, reflecting a degree of optimism in industry sector) exploiting not only scalar values of the indices but also the trajectories/shapes of functions describing the indices. Thus our considerations may be helpful in constructing a better economic barometer. As far as we know, this is the first comparison of functional classifiers with respect to a criterion of their usefulness in economic applications. The main result of the paper is a presentation of how a small fraction of outliers in a training sample, which are linearly independent from the training sample, consisting of almost linearly dependent functions, corrupt all analysed classifiers.

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“…Typically, multivariate functional data are obtained from two sources: combining raw univariate curves and their derivatives (Cuevas et al (2007) functional data with multiple responses (Hubert et al (2016) and Hubert et al (2015)). We conducted simulation studies on both sources.…”

Section: Multivariate Functional Datamentioning

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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Multivariate and functional classification using depth and distance

Cited by 48 publications

References 54 publications

New distance measures for classifying X-ray astronomy data into stellar classes

New distance measures for classifying X-ray astronomy data into stellar classes

A Critical Study of Usefulness of Selected Functional Classifiers in Economics

An Outlyingness Matrix for Multivariate Functional Data Classification

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