Manifold Denoising

By Matthias Hein, Markus Maier. 2006

209 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Geometry and Topology

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Citations in the corpus

PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examples (2017, methodology): “…also present in other machine learning methods not speciﬁcally designed for handling adversarial data; for example, the manifold denoising method of Hein & Maier (2007), the direct density gradient estimation of Sasaki et al. (2014), and the denoising autoencoders of Vincent et al. (2008) all…”
Manifold Regularized Sparse NMF for Hyperspectral Unmixing (2013, background): “This assumption is referred to as manifold assumption, which can be applied in several image processing fields such as hyperspectral image classification [28], hyperspectral imagery representation [29], and manifold denoising [30].”
Label Efficient Semi-Supervised Learning via Graph Filtering (2019, methodology): “[26] proposed manifold denoising (MD) by using feature smoothing as a preprocessing step for semisupervised learning, where the denoised data features are used to construct a graph for running a label propagation algorithm.”
Hierarchical Subquery Evaluation for Active Learning on a Graph (2014, background): “If there are labeled datapoints it can be learned [40], alternatively it can be defined per dimension, based on the average distance between all neighbors [4], local distance [12], or by direct optimization [33].”
Semi-supervised learning by disagreement (2010, unknown): “Hein and Maier [39] attempted to remove noisy data and hence obtained a better graph.”
Introduction to Semi-Supervised Learning (2009, unknown): “The graph construction itself is important [11, 83, 82, 29, 167, 196].”
Finding and Leveraging Structure in Learning Problems (2012, background): “that focuses on aspects of the manifold not related to homology; see for instance [Hein and Maier, 2006] and references therein.”
Nonlinear Dimensionality Reduction with Local Spline Embedding (2009, background): “The utility of manifold learning has been demonstrated in many applications such as visualization [6], [50], [20], image analysis [11], image superresolution [8], denoising [25], motion analysis [26], data ranking [62], semisupervised learning [52], and so on.”
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing (2008, methodology): “Since most previous methods are sensitive to noise, it is essential to denoise the manifold data to project it onto a submanifold [25].”
Learning Context-Sensitive Shape Similarity by Graph Transduction (2010, unknown): “approximation [25], and adaptive kernel size selection [38].”
A brief introduction to weakly supervised learning (2018, background): “Apparently, the performance will heavily depends on how the graph is constructed [14, 39, 77].”