Modern Multidimensional Scaling: Theory and Applications

By I. Borg, A. O’Connell, Patrick J. F. Groenen. 1999

Subfields: Representation & Self-Supervised Learning

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Citations in the corpus

Local Aggregation for Unsupervised Learning of Visual Embeddings (2019, methodology): “To further illustrate this point, we use the multi-dimensional scaling (MDS) algorithm [4] to visualize part of the embedding space (see Fig.”
Supervised Dimensionality Reduction via Distance Correlation Maximization (2016, methodology): “Given matrices (cid:98) E X , (cid:98) E Y , and column centered matrices (cid:101) X , (cid:101) Y , from result of Torgerson [1952] we have that (cid:98) E In the problem of multidimensional scaling (MDS) [Borg and Groenen, 2005], we know for a given adjacency matrix say W and a Laplacian matrix L”
Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions (2011, methodology): “This can be done using multidimensional scaling (MDS) (Borg and Groenen, 2005), isomap (Tenenbaum et al., 2000), curvilinear component analysis (Sun et al., 2010) or other methods that require only the pairwise distances.”
Out-of-Domain Detection for Natural Language Understanding in Dialog Systems (2019, methodology): “The MDS algorithm (Borg and Groenen, 2003) was used to map (a) MSP”
Computational Optimal Transport (2018, methodology): “2] using simple methods such as multidimensional scaling [Borg and Groenen, 2005].”
Sex differences in value priorities: cross-cultural and multimethod studies. (2005, methodology): “To assess meaning equivalence, we conducted separate MDS analyses (Borg & Groenen, 1997; Guttman, 1968) of the value items for men and for women in the French, German, and Italian samples.”
Analysis of stock market indices through multidimensional scaling (2011, background): “The result is the transformation of the data into similarity measures which can be represented by Euclidean distances in a space of unknown dimensions [4].”
The characteristics of sexual abuse in sport: A multidimensional scaling analysis of events described in media reports (2008, methodology): “389 lish a respected role among the community in order to conceal their unethical behavior (Brackenridge, 1997; Cense & Brackenridge, 2001). Other studies have examined the environmental or contextual variables surrounding the abuse. Myers and Barrett (2002) conducted visual inspection of 78 cases f”
A Review of Feature Selection and Feature Extraction Methods Applied on Microarray Data (2015, methodology): “A similar linear approach is classical multidimensional scaling (classical MDS) or Principal Coordinates Analysis [68] which calculates the matrix of dissimilarities for any given matrix input.”
MUFOLD: A new solution for protein 3D structure prediction (2010, methodology): “This is made possible by a much faster graph-based method, multidimensional scaling (MDS)22 in coarse-grain model generation than the time-consuming optimization methods such as genetic algorithms and Monte Carlo optimizations by current popular servers.”
Smartphones Based Crowdsourcing for Indoor Localization (2015, unknown): “Multidimensional scaling [4] is a set of related statistical techniques often used in information visualization for exploring similarities or dissimilarities in data.”
Sensor positioning in wireless ad-hoc sensor networks using multidimensional scaling (2004, methodology): “X is randomly initialized as X [0] and will be updated into X ([1]), X ([2]), X [3] .”
Multidimensional Scaling Using Majorization: SMACOF in R (2008, methodology): “Further speciﬁcations of this partially restricted framework can be found in De Leeuw and Heiser (1980) and additional elaborations in Borg and Groenen (2005, Chapter 10).”
Spacing Loss for Discovering Novel Categories (2022, methodology): “The proof of this inequality follows [4, 7].”
Learning Actionable Representations with Goal-Conditioned Policies (2018, methodology): “MDS is a technique that projects points from a high dimensional space into 2-”