Distance-based linear discriminant analysis for interval-valued data

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• 作者：Ana B. Ramos-Guajardo ; ^a ; ^{ramosana@uniovi.es" class="auth_mail" title="E-mail the corresponding author} ; Przemyslaw Grzegorzewski^b ; ^{pgrzeg@ibspan.waw.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Classification ; Discriminant analysis ; Interval data ; LDA ; Random intervals
• 刊名：Information Sciences
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：372
• 期：Complete
• 页码：591-607
• 全文大小：966 K

文摘

Interval-valued observations arise in many real-life situations as either the precise representation of the objective entity or the representation of incomplete knowledge. Thus given p   features observed over a sample of objects belonging to one of two possible classes, each observation can be perceived as a non-empty closed and bounded hyperrectangle on Rp${\mathbb{R}}^p$. The aim of the paper is to suggest a p-dimensional classification method for random intervals when two or more classes are considered, by the generalization of Fisher’s procedure for linear discriminant analysis. The idea consists of finding a directional vector which maximizes the ratio of the dispersion between the classes and within the classes of the observed hyperrectangles. A classification rule for new observations is also provided and some simulations are carried out to compare the behavior of the proposed classification procedure with respect to other methods known from the literature. Finally, the suggested methodology are applied on a real-life situation example.