Multidimensional Scaling, Second Edition

By T. Cox, M. Cox. 2000

399 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ac1da39b47f025d5e133b442283b50b1a3c4610e

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In Mechanical Engineering

Citations in the corpus

Large-scale manifold learning (2008, methodology): “Before generating low-dimensional embeddings in Isomap, one needs to convert distances into similarities using a process called centering [5].”
Big data and artificial intelligence in the maritime industry: a bibliometric review and future research directions (2020, methodology): “Although Bibliometrix offers a few alternatives, we used the multidimensional scaling (MDS) method (Cox and Cox 2000) for information visualisation and the Louvain clustering algorithm (Blondel et al. 2008) for detecting communities in networks.”
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks (2018, methodology): “The original problem dimension of 231 is reduced using a generalized version of the classical multidimensional scaling method [56].”
Partial Distance Correlation with Methods for Dissimilarities (2013, neutral): “t is well known in (metric) multidimensional scaling. Mardia, Kent, and Bibby [19] summarize the result in Theorem 14.2.1, and provide a proof. For an overview of the methodology see also Cox and Cox [3], Gower [7], Mardia [18], and Torgerson [35]. We apply the converse (b) of Theorem 14.2.1 as stat”
Estimating morphological diversity and tempo with discrete character‐taxon matrices: implementation, challenges, progress, and future directions (2016, background): “Principal coordinates can be thought of as a special case of classic (or metric) multidimensional scaling (Cox & Cox, 2001) where the number of ordination axes is maximized at N – 1, where N is the number of objects (taxa).”
Why Do Similarity Matching Objectives Lead to Hebbian/Anti-Hebbian Networks? (2017, background): “One can understand intuitively that the objective (2) is optimized by the projection onto the principal subspace by considering the following (for a rigorous proof see (Pehlevan and Chklovskii, 2015; Mardia et al., 1980; Cox and Cox, 2000)).”
Semantic Proximity Search on Heterogeneous Graph by Proximity Embedding (2017, methodology): “, earlier methods, such as MDS (Cox and Cox 2000), LLE (Roweis and Saul 2000), IsoMap (Tenenbaum, de Silva, and Langford 2000) and Laplacian eigenmap (Belkin and Niyogi 2001), typical rely on eigendecomposition of the graph affinity matrices to find the leading eigenvectors as each node’s embedding.”
A new embedding quality assessment method for manifold learning (2011, methodology): “Classical linear methods, such as Principal Component Analysis (PCA) [2], [3] and Multidimensional Scaling (MDS) [4], achieve their success under the assumption that data lie in a linear subspace.”
Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling (2010, background): “Multi-dimensional scaling (MDS) allows gaining insight in the complex relationship among patterns by providing a geometrical representation of their similarities (Cox and Cox, 2001).”
From Node Embedding To Community Embedding (2016, methodology): “d Work There is no existing graph embedding work that considers community embedding. Most of the graph embedding methods focus on generating node embedding. For example, earlier methods, such as MDS (Cox and Cox 2000), LLE (Roweis and Saul 2000), IsoMap (Tenenbaum, de Silva, and Langford 2000) and L”