A Nonlinear Mapping for Data Structure Analysis

By Jr. J. W. Sammon, John W. Sammon Jr.. 1969

Subfields: Representation & Self-Supervised Learning

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In Representation & Self-Supervised Learning

Citations in the corpus

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.”
A practical tutorial on autoencoders for nonlinear feature fusion: Taxonomy, models, software and guidelines (2018, background): “Sammon mapping [102] modifies the classical cost function of MDS, in an attempt to similarly weigh retaining large distances as well as small ones.”
Hierarchical Stochastic Neighbor Embedding (2016, methodology): “Algorithms such as Sammon Mapping [Sam69], LLE [RS00], ISOMAP [TDSL00] or tSNE [vdMH08] help during Exploratory Data Analysis by giving a meaningful representation of these high-dimensional spaces.”
Artificial Neural Networks — ICANN 2001 (2001, methodology): “However, as Rf is the radius of the ball containing the examples in the feature space [17], it only depends on the chosen kernel and not on k.”
T-SNE-CUDA: GPU-Accelerated T-SNE and its Applications to Modern Data (2018, methodology): “In addition to t-SNE, other methods have been explored by data scientists and vision researchers to visualize high dimensional data such as Sammon Mapping [24], Isomap [26], Locally Linear Embedding [21], Randomized Principle Component Analysis [20] and Johnson-Lindenstrauss Embedding [12].”
Texture Mapping Using Surface Flattening via Multidimensional Scaling (2002, methodology): “Motivated by [28] we introduce a new efficient mapping method that preserves both the local and the global structure of the texture, with minimal shearing effects.”
Dimensionality Reduction: A Comparative Review (2008, methodology): “In this subsection, we discuss one such MDS variant called Sammon mapping [108].”
Evolving plastic neural networks with novelty search (2010, methodology): “Two potential such visualization techniques are Principal Component Analysis (PCA; Kittler & Young, 1973) and Sammon’s mapping (Sammon, 1969).”
Comparisons among clustering techniques for electricity customer classification (2006, methodology): “The Sammon map [23] overcomes the PCA limits by performing a nonlinear projection that preserves the topology of”
Visualization of image data from cells to organisms (2010, unknown): “A common strategy linearly projects high-dimensional data into low dimensions for visualization using various forms of multidimensional scaling 60 (for example, principal component analysis, Sammon mapping 61 ).”
Icasso: software for investigating the reliability of ICA estimates by clustering and visualization (2003, background): “However, for |rij | the same transformation is not guaranteed to give a distance matrix that would exactly originate from Euclidean distances between points in Rk.”
On a Connection between Kernel PCA and Metric Multidimensional Scaling (2004, methodology): “An early reference to this kind of method is Sammon (1969) [6], where wii = 1/c5ii and f is the identity function.”
GPU accelerated t-distributed stochastic neighbor embedding (2019, methodology): “A significant number of techniques have been proposed to do such dimensionality reduction with classical methods such as principal component analysis [13], [14], multi-dimensional scaling [15], and more modern methods such as Sammon mapping [16], curvilinear component analysis [17], stochastic neigh”