Least-squares bilinear clustering of three-way data

Pieter C. Schoonees (), Patrick J. F. Groenen () and Michel Velden ()
Additional contact information
Pieter C. Schoonees: Erasmus University
Patrick J. F. Groenen: Erasmus University Rotterdam
Michel Velden: Erasmus University Rotterdam

Advances in Data Analysis and Classification, 2022, vol. 16, issue 4, No 8, 1037 pages

Abstract: Abstract A least-squares bilinear clustering framework for modelling three-way data, where each observation consists of an ordinary two-way matrix, is introduced. The method combines bilinear decompositions of the two-way matrices with clustering over observations. Different clusterings are defined for each part of the bilinear decomposition, which decomposes the matrix-valued observations into overall means, row margins, column margins and row–column interactions. Therefore up to four different classifications are defined jointly, one for each type of effect. The computational burden is greatly reduced by the orthogonality of the bilinear model, such that the joint clustering problem reduces to separate problems which can be handled independently. Three of these sub-problems are specific cases of k-means clustering; a special algorithm is formulated for the row–column interactions, which are displayed in clusterwise biplots. The method is illustrated via an empirical example and interpreting the interaction biplots are discussed. Supplemental materials for this paper are available online, which includes the dedicated R package, lsbclust.

Keywords: Three-way data; Bilinear decomposition; k-Means cluster analysis; Least-squares estimation; Biplots; 62H30; 15A18 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11634-021-00475-2 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:advdac:v:16:y:2022:i:4:d:10.1007_s11634-021-00475-2

Ordering information: This journal article can be ordered from
http://www.springer. ... ds/journal/11634/PS2

DOI: 10.1007/s11634-021-00475-2

Access Statistics for this article

Advances in Data Analysis and Classification is currently edited by H.-H. Bock, W. Gaul, A. Okada, M. Vichi and C. Weihs

More articles in Advances in Data Analysis and Classification from Springer, German Classification Society - Gesellschaft für Klassifikation (GfKl), Japanese Classification Society (JCS), Classification and Data Analysis Group of the Italian Statistical Society (CLADAG), International Federation of Classification Societies (IFCS)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().