Results 291 to 300 of about 493,672 (330)

Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction

arXiv.org
Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections onto the first few leading principal components of the training data ...
Paul Schwerdtner, Benjamin Peherstorfer
semanticscholar   +1 more source

Reconstructible Nonlinear Dimensionality Reduction via Joint Dictionary Learning

IEEE Transactions on Neural Networks and Learning Systems, 2019
This paper presents a parametric low-dimensional (LD) representation learning method that allows to reconstruct high-dimensional (HD) input vectors in an unsupervised manner.
Xian Wei, Hao Shen, Yuanxiang Li, Xuan Tang, Fengxiang Wang, M. Kleinsteuber, Y. Murphey   +6 more
semanticscholar   +1 more source

Semi-supervised nonlinear dimensionality reduction

Proceedings of the 23rd international conference on Machine learning - ICML '06, 2006
The problem of nonlinear dimensionality reduction is considered. We focus on problems where prior information is available, namely, semi-supervised dimensionality reduction. It is shown that basic nonlinear dimensionality reduction algorithms, such as Locally Linear Embedding (LLE), Isometric feature mapping (ISOMAP), and Local Tangent Space Alignment (
Xin Yang, Haoying Fu, Hongyuan Zha, Jesse Barlow   +3 more
openaire   +1 more source

Nonlinear Dimensionality Reduction by Locally Linear Inlaying

IEEE Transactions on Neural Networks, 2009
High-dimensional data is involved in many fields of information processing. However, sometimes, the intrinsic structures of these data can be described by a few degrees of freedom. To discover these degrees of freedom or the low-dimensional nonlinear manifold underlying a high-dimensional space, many manifold learning algorithms have been proposed ...
Yuexian, Hou, Peng, Zhang, Xingxing, Xu, Xiaowei, Zhang, Wenjie, Li   +4 more
openaire   +2 more sources

Incremental nonlinear dimensionality reduction by manifold learning

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006
Understanding the structure of multidimensional patterns, especially in unsupervised cases, is of fundamental importance in data mining, pattern recognition, and machine learning. Several algorithms have been proposed to analyze the structure of high-dimensional data based on the notion of manifold learning.
Martin H C, Law, Anil K, Jain
openaire   +2 more sources

Dimensional Reduction for Nonlinear Boundary Value Problems

SIAM Journal on Numerical Analysis, 1988
The paper describes a dimension reduction method for a class of strongly nonlinear boundary value problems. The idea is to choose a priori a basis of functions for one of the variables by ways of asymptotic expansions. Numerical experiments are presented.
Jensen, Soren, Babuška, Ivo
openaire   +1 more source

Locally Adaptive Nonlinear Dimensionality Reduction

2006
Popular nonlinear dimensionality reduction algorithms, e.g., SIE and Isomap suffer a difficulty in common: global neighborhood parameters often fail in tackling data sets with high variation in local manifold. To improve the availability of nonlinear dimensionality reduction algorithms in the field of machine learning, an adaptive neighbors selection ...
Yuexian Hou, Hongmin Yang, Pilian He
openaire   +1 more source

Nonlinear Dimensionality Reduction for Visualization

2013
The visual interpretation of data is an essential step to guide any further processing or decision making. Dimensionality reduction (or manifold learning) tools may be used for visualization if the resulting dimension is constrained to be 2 or 3. The field of machine learning has developed numerous nonlinear dimensionality reduction tools in the last ...
Michel Verleysen, John A. Lee
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DISCRIMINATIVE NONLINEAR DIMENSIONALITY REDUCTION FOR IMPROVED CLASSIFICATION

International Journal of Neural Systems, 1994
Multi-Layer Perceptron (MLP) neural networks have been used extensively for classification tasks. Typically, the MLP network is trained explicitly to produce the correct classification as its output. For speech recognition, however, several investigators have recently experimented with an indirect approach: a unique MLP predictive network is trained ...
openaire   +2 more sources

Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows

arXiv.org, 2017
Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference.
R. Mojgani, Maciej Balajewicz
semanticscholar   +1 more source