Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

By Joseph B. Kruskal. 1964

Subfields: Representation & Self-Supervised Learning

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In Representation & Self-Supervised Learning

Citations in the corpus

Inductive Representation Learning on Large Graphs (2017, neutral): “We ﬁrst describe the GraphSAGE embedding generation (i.e., forward propagation) algorithm, which generates embeddings for nodes assuming that the GraphSAGE model parameters are already learned (Section 3.1).”
UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (2018, methodology): “Algorithms such as PCA [8], MDS [9], and Sammon mapping [20] fall into the former category while t-SNE [15] [26], Isomap [24], LargeVis [22], Laplacian eigenmaps [1] [2], diffusion maps [4], NeRV [28], and JSE [12] all fall into the latter category.”
What Does BERT Look at? An Analysis of BERT’s Attention (2019, methodology): “Using these distances, we visualize the attention heads by applying multidimensional scaling (Kruskal, 1964) to embed each head in two dimensions such that the Euclidean distance between embeddings reﬂects the Jensen-Shannon distance between the corresponding heads as closely as possible.”
Deep learning via semi-supervised embedding (2008, background): “Multidimensional scaling (MDS) [16] is a classical algorithm that attempts to preserve the distance between points, whilst embedding them in a lower dimensional space, e.”
Representation Learning on Graphs: Methods and Applications (2017, methodology): “Early methods for learning representations for nodes largely focused on matrix-factorization approaches, which are directly inspired by classic techniques for dimensionality reduction [4, 36].”
A Survey of Inductive Biases for Factorial Representation-Learning (2016, background): “MDS creates a Cartesian space in which distance between the pair is reflective of similarity ratings from humans.”
State Representation Learning in Robotics: Using Prior Knowledge about Physical Interaction (2014, methodology): “Note that this problem is more difficult than the standard dimensionality reduction problem, addressed by multi-dimensional scaling [14] and other methods [23, 29, 6] because they require knowledge of distances or neighborhood relationships between data samples in state space.”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, background): “Isotonic regression has several applications in machine learning and statistics, where these monotonic constraints are relevant, for example in genetics [138], biology [176], medicine [186], statistics [17] and multidimensional scaling for psychology applications [128].”
Quality assessment of dimensionality reduction: Rank-based criteria (2009, background): “This is a fundamental difference, compared to older quality criteria that classically quantify the preservation of pairwise distances, with a stress function [17,29].”
Euclidean Distance Geometry and Applications (2012, methodology): “The next important step was given by Kruskal [112, 113], who puts Shepard’s ideas on a formal way in terms of optimization of a least squares function.”
A historical review of recurrence plots (2008, background): “The work of Kruskal in the 1960s [23] was one of the most quoted works in statistics and deeply affected many fields of investigation from ecology to psychology and economics.”
Computational Intelligence and Feature Selection - Rough and Fuzzy Approaches (2008, methodology): “This led to the development of nonmetric MDS to allow for these possibilities and additionally enabling the use of ordinal data [188,326].”
Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models (2005, methodology): “In Figure 1(c) we show the result of non-metric MDS using the stress criterion of Kruskal (1964).”