Mapping a manifold of perceptual observations
J Tenenbaum - Advances in neural information processing …, 1997 - proceedings.neurips.cc
Nonlinear dimensionality reduction is formulated here as the problem of trying to find a
Euclidean feature-space embedding of a set of observations that preserves as closely as …
Euclidean feature-space embedding of a set of observations that preserves as closely as …
Nonlinear dimension reduction via local tangent space alignment
In this paper we present a new algorithm for manifold learning and nonlinear dimension
reduction. Based on a set of unorganized data points sampled with noise from the manifold …
reduction. Based on a set of unorganized data points sampled with noise from the manifold …
Charting a manifold
M Brand - Advances in neural information processing …, 2002 - proceedings.neurips.cc
We construct a nonlinear mapping from a high-dimensional sample space to a low-
dimensional vector space, effectively recovering a Cartesian coordinate system for the …
dimensional vector space, effectively recovering a Cartesian coordinate system for the …
A global geometric framework for nonlinear dimensionality reduction
JB Tenenbaum, V Silva, JC Langford - science, 2000 - science.org
Scientists working with large volumes of high-dimensional data, such as global climate
patterns, stellar spectra, or human gene distributions, regularly confront the problem of …
patterns, stellar spectra, or human gene distributions, regularly confront the problem of …
Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
We present a new algorithm for manifold learning and nonlinear dimensionality reduction.
Based on a set of unorganized data points sampled with noise from a parameterized …
Based on a set of unorganized data points sampled with noise from a parameterized …
[PDF][PDF] Dimensionality reduction a short tutorial
A Ghodsi - … of Statistics and Actuarial Science, Univ …, 2006 - people.computing.clemson.edu
Manifold learning is a significant problem across a wide variety of information processing
fields including pattern recognition, data compression, machine learning, and database …
fields including pattern recognition, data compression, machine learning, and database …
[PDF][PDF] Think globally, fit locally: unsupervised learning of low dimensional manifolds
The problem of dimensionality reduction arises in many fields of information processing,
including machine learning, data compression, scientific visualization, pattern recognition …
including machine learning, data compression, scientific visualization, pattern recognition …
Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
DL Donoho, C Grimes - Proceedings of the National …, 2003 - National Acad Sciences
We describe a method for recovering the underlying parametrization of scattered data (mi)
lying on a manifold M embedded in high-dimensional Euclidean space. The method …
lying on a manifold M embedded in high-dimensional Euclidean space. The method …
A spatio-temporal extension to isomap nonlinear dimension reduction
OC Jenkins, MJ Matarić - Proceedings of the twenty-first international …, 2004 - dl.acm.org
We present an extension of Isomap nonlinear dimension reduction (Tenenbaum et al., 2000)
for data with both spatial and temporal relationships. Our method, ST-Isomap, augments the …
for data with both spatial and temporal relationships. Our method, ST-Isomap, augments the …
Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets
P Demartines, J Hérault - IEEE Transactions on neural …, 1997 - ieeexplore.ieee.org
We present a new strategy called" curvilinear component analysis"(CCA) for dimensionality
reduction and representation of multidimensional data sets. The principle of CCA is a self …
reduction and representation of multidimensional data sets. The principle of CCA is a self …