Unsupervised Learning of Image Manifolds by Semidefinite Programming

By Kilian Q. Weinberger, Lawrence K. Saul. Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., 2004

1,037 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/8f70d8019618a7c1dfc8118711a2e72ea5a510e7

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Citations in the corpus

Disentangled Person Image Generation (2017, background): “In particular, in [34, 30, 35, 5] it has been shown that they lie on or near a low-dimensional manifold of the original highdimensional space.”
Linear dimensionality reduction: survey, insights, and generalizations (2014, methodology): “…are nonlinear manifold methods, the most popular of which include Local Linear Embedding (Roweis and Saul, 2000), Isomap (Tenenbaum et al., 2000), Laplacian eigenmaps (Belkin and Niyogi, 2003), maximum variance unfolding (Weinberger and Saul, 2006) and diffusion maps (Coifman and Lafon, 2006).”
Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms (2013, methodology): “Maximum Variance Unfolding (MVU) [40] is a graph-based method that computes the low-dimensional representation by explicitly attempting to 'unfold' the high-dimensional data manifold, as in Figure 4.”
Unsupervised Feature Learning and Deep Learning: A Review and New Perspectives (2012, methodology): “…Isomap (Tenenbaum et al. , 2000), Laplacian Eigenmap (Belkin and Niyogi, 2003), Hessian Eigenmaps (Donoho and Grimes, 2003), Semideﬁnite Embedding (Weinberger and Saul, 2004), SNE (Hinton and Roweis, 2003) and t-SNE (van der Maaten and Hinton, 2008) that were primarily developed and used for data…”
Sparse Manifold Clustering and Embedding (2011, methodology): “Global methods, such as Isomap [4], Semidefinite embedding [5], Minimum volume embedding [6] and Structure preserving embedding [7], try to preserve local and global relationships among all data points.”
The Elastic Embedding Algorithm for Dimensionality Reduction (2010, methodology): “Work supported by NSF CAREER award IIS–0754089.”
Speedup Matrix Completion with Side Information: Application to Multi-Label Learning (2013, background): “It has broad applications including collaborative filtering [35], dimensionality reduction [41], multi-class learning [4, 31], clustering [15, 42], etc.”
Visualizing Similarity Data with a Mixture of Maps (2007, methodology): “Local MDS [8] and some more recent methods such as local linear embedding (LLE) [7], maximum variance unfolding [10], or stochastic neighbour embedding (SNE) [3] attempt to model local distances (strong similarities) accurately in the two-dimensional visualization at the expense of modeling larger d”
Massively parallel unsupervised single-particle cryo-EM data clustering via statistical manifold learning (2016, neutral): “To date, several nonlinear manifold learning frameworks have been proposed, such as isometric feature mapping (Isomap) [28,30–32], generative topographic mapping (GTM) [33–35], locally linear embedding (LLE) [29,36,37], and semidefinite embedding (SDE) [38].”
Shift-invariant similarities circumvent distance concentration in stochastic neighbor embedding and variants (2011, background): “Isomap [14], locally linear embedding [15], maximum variance unfolding [16], and other manifold learners based e.”
Semi-Supervised and Unsupervised Deep Visual Learning: A Survey (2022, background): “Semi-supervised learning [7], [8] and unsupervised learning [9], [10], [11], [12] stand out as two most representative paradigms for leveraging unlabeled data.”
Towards the Augmented Pathologist: Challenges of Explainable-AI in Digital Pathology (2017, background): “This is highly relevant for many applications in machine learning where we are confronted with high-dimensional data and to find meaningful representations in the lower-dimensions (Tenenbaum et al., 2000; Saul and Roweis, 2003; Weinberger and Saul, 2006).”
An Introduction to Nonlinear Dimensionality Reduction by Maximum Variance Unfolding (2006, background): “Here we show some solutions (Weinberger & Saul 2004; Blitzer et al. 2005) that are particularly easy to visualize.”
Learning a kernel matrix for nonlinear dimensionality reduction (2004, methodology): “This paper focuses mainly on its interpretation as a kernel method, while a companion paper (Weinberger & Saul, 2004) focuses on its application to the unsupervised learning of image manifolds.”
Discriminative Autoencoders for Small Targets Detection (2014, methodology): “Other approaches learn the manifold in a global way, such as the Maximum Variant Unfolding [25], or autoencoders [26].”
A Simpler Approach to Matrix Completion (2009, background): “1 Introduction Recovering a low rank matrix from a given subset of its entrie s is a recurring problem in collaborative filtering [25], dimensionality reduction [20, 28], and multi-class learni ng [2, 22].”
Dimensionality Reduction by Learning an Invariant Mapping (2006, background): “in [11, 12] attempt to learn the kernel matrix when the high dimensional input lies on a low dimensional manifold by formulating the problem as a semidefinite program.”
Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction (2006, background): “Although several non-linear dimensionality reduction techniques have been proposed (especially in the context of image analysis [34], speech recognition [35], visualizing word usages [36], climate data analysis [37, 38]) the development of new methods is still an active area of research.”