Principal manifolds and nonlinear dimensionality reduction via tangent space alignment

By Zhenyue Zhang, Hongyuan Zha. 2004

1,664 citations recorded by the source corpus.

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

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Citations in the corpus

Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions (2011, background): “…embedding and manifold learning (Roweis and Saul, 2000) are well studied problems; several diﬀerent algorithms have been proposed for this problem (Borg and Groenen, 2005, Tenenbaum et al., 2000, Sun et al., 2010, Zhang and Zha, 2004, Belkin and Niyogi, 2003, Donoho and Grimes, 2003).”
Image Clustering Using Local Discriminant Models and Global Integration (2010, background): “Previous manifold learning algorithms [1] [28] [46] and clustering algorithms [29] [38] [47] have demonstrated that it is beneficial to exploit local geometric properties for recovering the intrinsic manifold structure of data.”
Toward a Quantitative Survey of Dimension Reduction Techniques (2019, methodology): “…Locally Linear Embedding ( LLE )[65] and its variants Hessian LLE ( H-LLE ) [66], Modiﬁed LLE ( M-LLE ) [67] and Local Tangent Space Alignment ( LTSA ) [68], Laplacian Eigenmaps ( LE ) [69], Diffusion Maps ( DM ) [70], Manifold Charting ( MC ) [71], and Local Linear Coordination ( LLC ) [72].”
Testing the Manifold Hypothesis (2013, neutral): “LTSA works for parameterized manifolds and detailed error analysis is available for it.”
Learning in high-dimensional multimedia data: the state of the art (2015, methodology): “Some other non-linear feature transformation methods include kernel PCA [76], Hessian LLE [14], Laplacian Eigenmaps [2], LTSA [102] and so on.”
Spectral Methods for Dimensionality Reduction (2006, neutral): “Other algorithms closely related to the ones covered here include hessian related work LLE [Donoho and Grimes, 2003], c-Isomap [de Silva and Tenenbaum, 2003], local tangent space alignment [Zhang and Zha, 2004], geodesic nullspace analysis [Brand, 2004], and conformal eigenmaps [Sha and Saul, 2005].”
A Semi-NMF-PCA Unified Framework for Data Clustering (2017, background): “…0 (cid:4) 1 weighting scheme to construct the k-nearest neighbor graph, and deﬁne the data weight matrix W as follows, The Laplacian embedding [3], [33] preserves the local geometrical relationships and maximizes the smoothness with respect to the intrinsic manifold of the data set in the…”