Learning a kernel matrix for nonlinear dimensionality reduction

By Kilian Q. Weinberger, Fei Sha, Lawrence K. Saul. 2004

595 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications (2017, background): “(4) AgLPP [79] anchor graph,W ¼ ZL 1ZT , Lkk ¼ P Zik, Zik ¼ Ks ðXi;UkÞP j Ks ðXi;UjÞ a ¼ argmin aT ULUT a aT UDUT a LGRM [98] KNN,Wij ¼ exp kXi Xjk2 2t2 y ¼ argmin y T ðLleþmLgÞy yT y ARE [88] KNN,Wij ¼ exp r2ðXiXjÞ t ,WAREij ¼ g; Xi 2 Fþ&Xj 2 Fþ 1;LðXiÞ 6¼ LðXjÞ 0; otherwise 8< : a ¼ argmax a T XLA”
Regression on Fixed-Rank Positive Semidefinite Matrices: A Riemannian Approach (2010, methodology): “Other kernel learning techniques include the maximum variance unfolding algorithm [Weinberger et al., 2004] and its semi-supervised version [Song et al., 2007], and the kernel spectral regression framework [Cai et al., 2007] which encompasses many reduction criterion (for example, linear…”
Transfer Learning via Dimensionality Reduction (2008, unknown): “However, there are two major differences between MMDE and colored MVU.”
Semidefinite Programming Approaches for Sensor Network Localization With Noisy Distance Measurements (2006, background): “Another approach is to allow a large radio range for every sensor so that they can communicate with many other sensors or anchors.”
Unsupervised Learning of Image Manifolds by Semidefinite Programming (2004, methodology): “In earlier work (Weinberger & Saul, 2004; Weinberger et al., 2004 ), we referred to this algorithm as “semidefinite embedding”, but here we will adopt the name “maximum variance unfolding” (MVU), coined by others (Sun et al., 2004), as it is both more descriptive and less likely to be confused with”
Learning Multiple Tasks using Manifold Regularization (2010, background): “Much recent work in manifold learning focused on uncovering low dimensional representation [18] [6] [17] [20] of the data.”
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.”
Nonlinear Dimensionality Reduction with Local Spline Embedding (2009, methodology): “…algorithms have been proposed, such as manifold charting [5], Laplacian Eigenmap (LE) [2], Hessian LLE (HLLE) [13], Local Tangent Space Alignment (LTSA) [61], semidefinite embedding [54], conformal eigenmap [45], and other extensive work [10], [22], [47], [38], [59], [60], [12], [16], [17], [37].”
Toward a Quantitative Survey of Dimension Reduction Techniques (2019, background): “Maximum Variance Unfolding (MVU) [81] and its variations Fast MVU (F-MVU) [82] and Landmark MVU ( L-MVU ) [83] aim to unfold the data manifold by maximizing euclidean distances between points while preserving pairwise distances in a neighborhood graph.”