# A survey of manifold learning and its applications for multimedia

arXiv: https://arxiv.org/abs/2310.12986 · HTML: https://mlsanity.com/paper/2310.12986/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 61 references that are in the map.
- First posted on arXiv 8 Sep 2023.

## Builds on (most cited first, 30 of 35)

- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [Embedding Propagation: Smoother Manifold for Few-Shot Classification](https://mlsanity.com/paper/2003.04151/) (2020)
- [Trivializations for Gradient-Based Optimization on Manifolds](https://mlsanity.com/paper/1909.09501/) (2019)
- [A Decade Survey of Content Based Image Retrieval using Deep Learning](https://mlsanity.com/paper/2012.00641/) (2020)
- [geomstats: a Python Package for Riemannian Geometry in Machine Learning](https://mlsanity.com/paper/1805.08308/) (2018)
- [Deep Learning for Instance Retrieval: A Survey](https://mlsanity.com/paper/2101.11282/) (2021)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Matching Normalizing Flows and Probability Paths on Manifolds](https://mlsanity.com/paper/2207.04711/) (2022)
- [Differentiating through the Fr'echet Mean](https://mlsanity.com/paper/2003.00335/) (2020)
- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)
- [Mining on Manifolds: Metric Learning without Labels](https://mlsanity.com/paper/1803.11095/) (2018)
- [Riemannian approach to batch normalization](https://mlsanity.com/paper/1709.09603/) (2017)
- [Manifold Topology Divergence: a Framework for Comparing Data Manifolds](https://mlsanity.com/paper/2106.04024/) (2021)
- [Projective Manifold Gradient Layer for Deep Rotation Regression](https://mlsanity.com/paper/2110.11657/) (2021)
- [LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihood](https://mlsanity.com/paper/2206.14882/) (2022)
- [Everything is There in Latent Space: Attribute Editing and Attribute Style Manipulation by StyleGAN Latent Space Exploration](https://mlsanity.com/paper/2207.09855/) (2022)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control](https://mlsanity.com/paper/1909.05946/) (2019)
- [Hierarchical Nearest Neighbor Graph Embedding for Efficient Dimensionality Reduction](https://mlsanity.com/paper/2203.12997/) (2022)
- [Manifold Optimization Over the Set of Doubly Stochastic Matrices: A Second-Order Geometry](https://mlsanity.com/paper/1802.02628/) (2018)
- [Dilated Convolutional Neural Networks for Sequential Manifold-valued Data](https://mlsanity.com/paper/1910.02206/) (2019)
- [Improving Metric Dimensionality Reduction with Distributed Topology](https://mlsanity.com/paper/2106.07613/) (2021)
- [ManifoldNorm: Extending normalizations on Riemannian Manifolds](https://mlsanity.com/paper/2003.13869/) (2020)
- [Directed Graph Embeddings in Pseudo-Riemannian Manifolds](https://mlsanity.com/paper/2106.08678/) (2021)

## Built on by (most cited first, 1 of 1)

- [Noisy Data Visualization using Functional Data Analysis](https://mlsanity.com/paper/2406.03396/) (2024)

## Abstract (arXiv)

Manifold learning is an emerging research domain of machine learning. In this work, we give an introduction into manifold learning and how it is employed for important application fields in multimedia.