Some Robust Distances for Multivariate Data

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Some Robust Distances for Multivariate Data

Popis výsledku v původním jazyce

Numerous methods of multivariate statistics and data mining suffer from the presence of outlying measurements in the data. This paper presents new distance measures suitable for continuous data. First, we consider a Mahalanobis distance suitable for high-dimensional data with the number of variables (largely) exceeding the number of observations. We propose its doubly regularized version, which combines a regularization of the covariance matrix with replacing the means of multivariate data by their regularized counterparts. We formulate explicit expressions for some versions of the regularization of the means, which can be interpreted as a denoising (i.e. robust version) of standard means. Further, we propose a robust cosine similarity measure, which is based on implicit weighting of individual observations. We derive properties of the newly proposed robust cosine similarity, which includes a proof of the high robustness in terms of the breakdown point.

Název v anglickém jazyce

Some Robust Distances for Multivariate Data

Popis výsledku anglicky

Numerous methods of multivariate statistics and data mining suffer from the presence of outlying measurements in the data. This paper presents new distance measures suitable for continuous data. First, we consider a Mahalanobis distance suitable for high-dimensional data with the number of variables (largely) exceeding the number of observations. We propose its doubly regularized version, which combines a regularization of the covariance matrix with replacing the means of multivariate data by their regularized counterparts. We formulate explicit expressions for some versions of the regularization of the means, which can be interpreted as a denoising (i.e. robust version) of standard means. Further, we propose a robust cosine similarity measure, which is based on implicit weighting of individual observations. We derive properties of the newly proposed robust cosine similarity, which includes a proof of the high robustness in terms of the breakdown point.

Druh

D - Stať ve sborníku

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the 34th International Conference Mathematical Methods in Economics MME 2016

ISBN

978-80-7494-296-9

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

365-370

Název nakladatele

Technical University

Místo vydání

Liberec

Místo konání akce

Liberec

Datum konání akce

6. 9. 2016

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000385239500063