Mapping a Manifold of Perceptual Observations

By Josh Tenenbaum. 1997

Subfields: Representation & Self-Supervised Learning

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Citations in the corpus

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (2018, neutral): “In comparison to previous techniques, including PCA [8], multidimensional scaling [9], and Isomap [23], t-SNE offers a dramatic improvement in finding and preserving local structure in the data. makes t-SNE the benchmark against which any dimension reduction technique must be compared.”
Conceptual and empirical comparison of dimensionality reduction algorithms (PCA, KPCA, LDA, MDS, SVD, LLE, ISOMAP, LE, ICA, t-SNE) (2021, unknown): “, The isomap algorithm and topological stability, Science, 295, 5552, 7 (2002) [46] Tenenbaum, J.”
Asymmetric metric learning for knowledge transfer (2020, background): “Metric learning Historically, metric learning is about unsupervised learning of embeddings according to a pairwise distances [65] or similarities [59, 3].”
Dimensionality reduction on Anchorgraph with an efficient Locality Preserving Projection (2016, methodology): “[8] proposed a method named Isomap, which aims at preserving the pairwise geodesic distances between data points by utilizing shortest-path algorithms.”
Unsupervised Large Graph Embedding (2017, methodology): “Most initial attempts are non-linear methods, e.g. LE (Belkin and Niyogi 2001), LLE (T and K 2000), and ISOMAP (Tenenbaum 1997).”
Stochastic Neighbor Embedding (2002, methodology): “Multidimensional scaling methods[1] preserve dissimilarities between items, as measured either by Euclidean distance, some nonlinear squashing of distances, or shortest graph paths as with Isomap[2, 3].”
Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds (2011, background): “Many unsupervised nonlinear dimensionality reduction techniques have been proposed in the last decade, including locally linear embedding (LLE) [53], Laplacian Eigenmaps [54], and Isomap [55].”
Global Versus Local Methods in Nonlinear Dimensionality Reduction (2002, background): “However, Tenenbaum [1] observed that such algorithms often fail when non-linear structure cannot simply be regarded as a perturbation from a linear approximation.”
Type 1 and 2 mixtures of Kullback-Leibler divergences as cost functions in dimensionality reduction based on similarity preservation (2013, methodology): “L. is a Research Associate with the Belgian h (F.R.S.-FNRS). a b s t r a c t Stochastic neighbor embedding (SNE) and its variants are methods of dimensionality reduction (DR) that involve normalized softmax similarities derived from pairwise distances.”
Super-resolution through neighbor embedding (2004, methodology): “These include isometric feature mapping (Isomap) [20, 21], locally linear embedding (LLE) [15, 16], and Laplacian eigenmap [3, 4].”
Continuous latent variable models for dimensionality reduction and sequential data reconstruction (2001, background): “Planning of paths through geodesics also offers interesting possibilities to applications where interpolation in data space is required, such as in morphing or animating an object from one three-dimensional configuration to another one (Bregler and Omohundro, 1995; Tenenbaum, 1998).”
A Bayesian framework for concept learning (1999, background): “These are exactly the sort ofstructures that many unsupervised learning algorithms are designed to discover inraw data (Duda & Hart, 1973; Shepard & Arabie, 1979; Tenenbaum, 1995, 1998).”
Dimensionality Reduction: A Comparative Review (2008, methodology): “If the high-dimensional data lies on or near a curved manifold, such as in the Swiss roll dataset [105], MDS might consider two datapoints as near points, whereas their distance over the manifold is much larger than the typical interpoint distance.”