Applications of Convex Analysis to Multidimensional Scaling

By Jan de Leeuw. 2000

430 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/45e288d93a674b10009ff0be9b7848b8d22493c8

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Citations in the corpus

Twister: a runtime for iterative MapReduce (2010, methodology): “K-Means[16], Deterministic Annealing Clustering[17], pagerank[18], and dimension reduction algorithms such as SMACOF[19] are all examples of such algorithms.”
Variations and extension of the convex–concave procedure (2016, methodology): “Expectation maximization was introduced in (Dempster et al, 1977) and although MM algorithms are just as old, as seen in (De Leeuw, 1977), the term majorization minimization was not coined until Hunter and Lange's rejoinder to (Lange et al, 2000).”
Multidimensional Scaling (2021, methodology): “There is a review of the early history, which starts with Carl Stumpf around 1880, in de Leeuw & Heiser (1980 a). Developments in psychophysics concentrated on specifying the shape of the function relating dissimilarities and distances, until Shepard (1962) made the radical proposal to let the data ”
Three-Dimensional Face Recognition (2005, methodology): “The algorithm using this multiplicative update is called SMACOF (De Leeuw, 1977; De Leeuw and Stoop, 1984; Borg and Groenen, 1997).”
A survey on data stream clustering and classification (2015, methodology): “Moreover, MC-Tree optimizes tree construction by using multi-dimensional scaling (MDS) [33] to transform the data space.”
Spherical and Hyperbolic Embeddings of Data (2014, background): “The optimization is an important step; here the stress majorization(SMACOF) algorithm has proved very popular [9], [10].”
Discrete Graph Hashing (2014, methodology): “The majorization method was first systematically introduced by [5] to deal with multidimensional scaling problems, although the EM algorithm [7], proposed at the same time, also falls into the framework of majorization methodology.”
Spacing Loss for Discovering Novel Categories (2022, methodology): “The proof of this inequality follows [4, 7].”
Multidimensional Scaling Using Majorization: SMACOF in R (2008, methodology): “Following De Leeuw (1977a), stress, as given in (4), can be decomposed as From restriction (5) it follows that the ﬁrst component η 2 δ = 1.”
On the Convergence of the Concave-Convex Procedure (2009, background): “This example shows that the same idea can be extended to any constraint set.”