Non-Linear Dimensionality Reduction

By David DeMers, Garrison W. Cottrell. 1992

Subfields: Representation & Self-Supervised Learning

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Citations in the corpus

Deep learning in neural networks: An overview (2014, background): “…(Lee & Kil, 1991), layer-wise UL of feature hierarchies fed into SL classifiers (Behnke, 1999, 2003a), the SelfOrganizing Tree Algorithm (SOTA) (Herrero, Valencia, & Dopazo, 2001), and nonlinear Autoencoders (AEs) with more than 3 (e.g., 5) layers (DeMers & Cottrell, 1993; Kramer, 1991; Oja, 1991).”
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders (2018, background): “Autoencoders (also known as auto-associators [21]) comprise a specific type of feedforward neural network that aim to learn the identity mapping: they attempt to copy the input to an accurate approximation of itself.”
Global Versus Local Methods in Nonlinear Dimensionality Reduction (2002, methodology): “These techniques include GTM [4], self organising maps [5] and others [6,7].”
Exploring Strategies for Training Deep Neural Networks (2009, background): “An example of such a non-linear unsupervised learning model is the autoassociator or autoencoder network (Cottrell et al., 1987; Saund, 1989; Hinton, 1989; Baldi and Hornik, 1989; DeMers and Cottrell, 1993).”
Face recognition: a convolutional neural-network approach (1997, methodology): “In [10] the first 50 principal components of the images are extracted and reduced to 5 dimensions using an autoassociative neural network.”
Dimensionality Reduction: A Comparative Review (2008, background): “Multilayer autoencoders Multilayer encoders are feed-forward neural networks with an odd number of hidden layers [33,54].”
Auto-encoder based dimensionality reduction (2016, background): “Dimensionality reduction is an old and young, dynamic research topic [11] [12].”
Feature Extraction Through LOCOCODE (1999, background): “and Zemel (1995), Li (1995), Olshausen and Field (1996), Zemel (1993), Hinton and Ghahramani (1997). Sparse codes share certain advantages of both local and dense codes. But what about coding costs? COCOFs express desirable properties of the code itself, while neglecting the costs of constructing th”
Neural Network Approaches to Image Compression (1995, background): “In experiments with real images , Cottrell and Munro achieved compression ratios of 1 : 8 with acceptable subjective levels of distortion .”
A Survey of Face Recognition Techniques (2009, methodology): “In [152], 50 principal components were extracted and an auto-associative neural network was used to reduce those components to five dimensions.”
Incremental nonlinear dimensionality reduction by manifold learning (2006, unknown): “Over time, different nonlinear mapping techniques have been proposed, such as self-organizing maps (SOM) [29], principal curve and its extensions [24], [28], [45], [47], auto-encoder neural networks [1], [ 15 ], generative topographic maps (GTM) [6] and kernel principal component analysis [42].”
Nonlinear ICA through low-complexity autoencoders (1999, methodology): “The results above give rise to a new method for source separation: simply train autoencoders (e.g., [2, 3, 4, 5 ]) via FMS.”