@inproceedings{0220246289884cde8081fea209bc10a5,

title = "Additive Trees for Fitting Three-Way (Multiple Source) Proximity Data",

abstract = "Additive trees are graph-theoretic models that can be used for constructing network representations of pairwise proximity data observed on a set of N objects. Each object is represented as a terminal node in a connected graph; the length of the paths connecting the nodes reflects the inter-object proximities. Carroll, Clark, and DeSarbo (J Classif 1:25–74, 1984) developed the INDTREES algorithm for fitting additive trees to analyze individual differences of proximity data collected from multiple sources. INDTREES is a mathematical programming algorithm that uses a conjugate gradient strategy for minimizing a least-squares loss function augmented by a penalty term to account for violations of the constraints as imposed by the underlying tree model. This article presents an alternative method for fitting additive trees to three-way two-mode proximity data that does not rely on gradient-based optimization nor on penalty terms, but uses an iterative projection algorithm. A real-world data set consisting of 22 proximity matrices illustrated that the proposed method gave virtually identical results as the INDTREES method.",

keywords = "Additive trees, Individual differences, Iterative projection, Three-way data",

author = "Koehn, {Hans Friedrich} and Kern, {Justin Louis}",

year = "2019",

doi = "10.1007/978-3-030-01310-3_35",

language = "English (US)",

isbn = "9783030013097",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "403--413",

editor = "Marie Wiberg and Steven Culpepper and Rianne Janssen and Jorge Gonz{\'a}lez and Dylan Molenaar",

booktitle = "Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018",

address = "Germany",

note = "83rd Annual meeting of the Psychometric Society, 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

}