Algorithms for manifold learning

By Lawrence Cayton. 2005

404 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning

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In Representation & Self-Supervised Learning

Citations in the corpus

Better Mixing via Deep Representations (2012, background): “…a fundamental problem of mixing : it is difﬁcult for the Markov chain to jump from one mode of the distribution to another, when these are separated by large low-density regions, a common situation in real-world data, and under the manifold hypothesis (Cayton, 2005; Narayanan and Mitter, 2010).”
A Generative Process for Contractive Auto-Encoders (2012, methodology): “A useful non-parametric modeling hypothesis for high dimensional data with a complicated structure, such as natural images or sounds, is the so-called manifold hypothesis (Cayton, 2005; Narayanan and Mitter, 2010; Rifai et al., 2011a).”
Representation Learning: A Review and New Perspectives (2012, background): “Its premise is the manifold hypothesis (Cayton, 2005; Narayanan and Mitter, 2010), according to which real-world data presented in high dimensional spaces are expected to concentrate in the vicinity of a manifold M of much lower dimensionality dM, embedded in high dimensional input space Rx .”
A practical tutorial on autoencoders for nonlinear feature fusion: Taxonomy, models, software and guidelines (2018, background): “The latter ones are usually known as manifold learning [34] algorithms, and fall in the scope of nonlinear dimensionality reduction techniques [35].”
Towards Deep Developmental Learning (2016, background): “Actually, the higher the dimensionality of the input space, the most likely this assumption [87], [88], [57].”
Salient Band Selection for Hyperspectral Image Classification via Manifold Ranking (2016, background): “a high-dimensional space is the feature space [14].”
The Manifold Tangent Classifier (2011, background): “The (unsupervised) manifold hypothesis, according to which real world data presented in high dimensional spaces is likely to concentrate in the vicinity of non-linear sub-manifolds of much lower dimensionality (Cayton, 2005; Narayanan and Mitter, 2010).”
Normalized Direction-preserving Adam (2017, background): “, images, audios, text) concentrates on manifolds of much lower dimensionality (Cayton, 2005; Narayanan & Mitter, 2010).”
Laplacian Auto-Encoders: An explicit learning of nonlinear data manifold (2015, background): “In many areas of machine learning and computer vision, a general assumption about sensory data is that they lie on or near a lowdimensional nonlinear manifold embedded in a high-dimensional space: when representing these data as points in a high-dimensional space, their probability density may be re”
Nonlinear Dimensionality Reduction with Local Spline Embedding (2009, background): “Actually, as pointed by Cayton [7], developing rigorous evaluation methodologies still remains elusive.”
Feature representation for statistical-learning-based object detection: A review (2015, neutral): “, ISOMAP, LLE, Laplacian Eigenmap [107]) is”
DISFA: A Spontaneous Facial Action Intensity Database (2013, background): “; yn 2 R (d << D), such that yi represents xi efficiently [64].”
Learning Hierarchical Priors in VAEs (2019, methodology): “To verify the quality of the latent representations, we build on the manifold hypothesis, defined in (Cayton, 2005; Rifai et al., 2011).”
Regularized Auto-Encoders Estimate Local Statistics (2012, background): “…being associated with an unknown target density function, denoted p. Manifold learning algorithms assume that p is concentrated in regions of lower dimension (Cayton, 2005; Narayanan and Mitter, 2010), i.e., the training examples are by definition located very close to these highdensity manifolds.”
MaxGain: Regularisation of Neural Networks by Constraining Activation Magnitudes (2018, background): “This is known as the manifold hypothesis [2].”
Decision Forests: A Unified Framework for Classification, Regression, Density Estimation, Manifold Learning and Semi-Supervised Learning (2012, background): “The interested reader is referred to some excellent surveys in [16, 18].”
Review of Bridge Structural Health Monitoring Aided by Big Data and Artificial Intelligence: From Condition Assessment to Damage Detection (2020, positive): “Nonlinear methods are more widely known as manifold learning (Cayton 2005) in recent years, which offer many choices for dimension reduction in datasets with nonlinear behaviors, e.g., using nonlinear PCA (NLPCA) to extract the main components induced by temperature and wind from modal parameters…”
Unsupervised Feature Learning and Deep Learning: A Review and New Perspectives (2012, background): “Its premise is the manifold hypothesis (Cayton, 2005; Narayanan and Mitter, 2010) according to which real-world data presented in high dimensional spaces are likely to concentrate in the vicinity of a non-linear manifold M of much lower dimensionality d M , embedded in high dimensional input space…”