Some Robust Distances for Multivariate Data
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F16%3A00462922" target="_blank" >RIV/67985807:_____/16:00462922 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—
Alternative languages
Result language
angličtina
Original language name
Some Robust Distances for Multivariate Data
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
—
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the 34th International Conference Mathematical Methods in Economics MME 2016
ISBN
978-80-7494-296-9
ISSN
—
e-ISSN
—
Number of pages
6
Pages from-to
365-370
Publisher name
Technical University
Place of publication
Liberec
Event location
Liberec
Event date
Sep 6, 2016
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
000385239500063