Multinomial Restricted Unfolding

Mark de Rooij () and Frank Busing ()
Additional contact information
Mark de Rooij: Leiden University
Frank Busing: Leiden University

Journal of Classification, 2024, vol. 41, issue 1, No 10, 190-213

Abstract: Abstract For supervised classification we propose to use restricted multidimensional unfolding in a multinomial logistic framework. Where previous research proposed similar models based on squared distances, we propose to use usual (i.e., not squared) Euclidean distances. This change in functional form results in several interpretational advantages of the resulting biplot, a graphical representation of the classification model. First, the conditional probability of any class peaks at the location of the class in the Euclidean space. Second, the interpretation of the biplot is in terms of distances towards the class points, whereas in the squared distance model the interpretation is in terms of the distance towards the decision boundary. Third, the distance between two class points represents an upper bound for the estimated log-odds of choosing one of these classes over the other. For our multinomial restricted unfolding, we develop and test a Majorization Minimization algorithm that monotonically decreases the negative log-likelihood. With two empirical applications we point out the advantages of the distance model and show how to apply multinomial restricted unfolding in practice, including model selection.

Keywords: Multiclass; Euclidean distance; Classification; Visualization (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00357-024-09465-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jclass:v:41:y:2024:i:1:d:10.1007_s00357-024-09465-3

Ordering information: This journal article can be ordered from
http://www.springer. ... hods/journal/357/PS2

DOI: 10.1007/s00357-024-09465-3

Access Statistics for this article

Journal of Classification is currently edited by Douglas Steinley

More articles in Journal of Classification from Springer, The Classification Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().