Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization

By Stéphane Lafon, Ann B. Lee. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006

688 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/06eb6b4566cbb127ebf548f251e9b89bf34777f2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Chunhua Shen
2. Anton van den Hengel
3. Pierre Vandergheynst
4. Shuicheng Yan
5. Pascal Frossard
6. Yoshua Bengio
7. Dacheng Tao
8. L. V. D. van der Maaten

In Computational Theory and Mathematics

1. Pierre Vandergheynst
2. Yuanyuan Ren
3. Peng Zhang
4. David I. Shuman
5. Ronald R. Coifman
6. Tong Lin
7. Hongyuan Zha
8. Stéphane Lafon

In Computer Vision and Pattern Recognition

1. Dacheng Tao
2. Chunhua Shen
3. Yi Yang
4. Luc Van Gool
5. Shuicheng Yan
6. Alan L. Yuille
7. Xiaogang Wang
8. Ming-Hsuan Yang

Citations in the corpus

• Riemannian Manifold Learning (2008, background): “Among the family of dimensionality reduction approaches, manifold learning1 algorithms have attracted extensive attention recently due to their nonlinear nature, geometric intuition, and computational feasibility.”
• Topology and data (2009, background): “• (Eigenvectors of graph Laplacians): Graph Laplacians are interesting linear operators attached to graphs (see [40]).”
• Hubs in Space: Popular Nearest Neighbors in High-Dimensional Data (2010, methodology): “, 2000), and diffusion maps (Lafon and Lee, 2006; Nadler et al., 2006).”
• Inductive Hashing on Manifolds (2013, positive): “IMH-DM is IMH with the diffusion maps of [18].”
• Crowded Scene Analysis: A Survey (2015, positive): “The key motion patterns are discovered using diffusion maps embedding [75] and clustering.”
• Data Fusion and Multicue Data Matching by Diffusion Maps (2006, methodology): “In this section, we recall the diffusion framework as described in [5], [12], [13].”
• A Multiscale Pyramid Transform for Graph Signals (2013, methodology): “Some examples include: 1) Lafon and Lee [32] cluster based on diffusion distances and form new edge weights based on random walk transition probabilities.”
• Dimensionality Reduction: A Comparative Review (2008, background): “, [68]) that the low-dimensional representation Y that retains the diffusion distances is formed by the d nontrivial principal eigenvectors of the eigenproblem”
• Transition Path Theory for Markov Jump Processes (2009, methodology): “glassy systems [3, 7] or biomolecules [28]), but also in the context of data segmentation and embedding [30, 21, 27, 4, 13, 10, 19].”
• A new embedding quality assessment method for manifold learning (2011, methodology): “Representative methods include Locally Linear Embedding (LLE) [5], [6], ISOMAP [7], [8], Laplacian Eigenmap (LE) [9], [10], Hessian LLE (HLLE) [11], Diffusion Maps (DM) [12], [13], Local Tangent Space Alignment (LTSA) [14], Maximum Variance Unfolding (MVU) [15], and Riemannian Manifold Learning…”
• Recent Advances in Graph Partitioning (2013, background): “Lafon and Lee [LL06] present a related coarsening framework whose goal is to retain the spectral properties of the graph.”