UMAP: Uniform Manifold Approximation and Projection

@article{McInnes2018UMAPUM,
  title={UMAP: Uniform Manifold Approximation and Projection},
  author={Leland McInnes and John Healy and Nathaniel Saul and Lukas Gro{\ss}berger},
  journal={J. Open Source Softw.},
  year={2018},
  volume={3},
  pages={861}
}
Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction. UMAP has a rigorous mathematical foundation, but is simple to use, with a scikit-learn compatible API. UMAP is among the fastest manifold learning implementations available – significantly faster than most t-SNE implementations. 
The mathematics of UMAP
TLDR
A comparison of UMAP embeddings with some other standard dimension reduction algorithms shows that UMAP gives similarly good outputs for visualisation as t-SNE, with a substantially better runtime, and may capture more of the global structure of the data.
Conditional Manifold Learning
  • A. Bui
  • Computer Science
    ArXiv
  • 2021
TLDR
A conditional version of the SMACOF algorithm is introduced to optimize the objective function of conditional multidimensional scaling.
EVALUATING UNIFORM MANIFOLD APPROXIMATION AND PROJECTION FOR DIMENSION REDUCTION AND VISUALIZATION OF POLINSAR FEATURES
TLDR
The results show that UMAP exceeds the capability of PCA and LE in these regards and is competitive with t-SNE.
Using Genetic Programming to Find Functional Mappings for UMAP Embeddings
TLDR
This work proposes utilising UMAP to create functional mappings with genetic programming-based manifold learning and compares two different approaches: one that uses the embedding produced by UMAP as the target for the functional mapping; and the other which directly optimises the UMAP cost function by using it as the fitness function.
Efficient Batch-Incremental Classification Using UMAP for Evolving Data Streams
TLDR
A batch-incremental approach that pre-processes data streams using UMAP, by producing successive embeddings on a stream of disjoint batches in order to support an incremental kNN classification.
Unsupervised Functional Data Analysis via Nonlinear Dimension Reduction
TLDR
A theoretical framework is defined which allows to systematically assess specific challenges that arise in the functional data context, several nonlinear dimension reduction methods for tabular and image data to functional data are transferred, and it is shown that manifold methods can be used successfully in this setting.
Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning
TLDR
Wasserstein Isometric Mapping is proposed, a parameter-free nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlineardimensionality reduction algorithms in imaging applications and yields good embeddings compared with other global techniques.
Deep Recursive Embedding for High-Dimensional Data
TLDR
This article proposes to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data embedding with a recursive strategy, called deep recursive embedding (DRE), to make use of the latent data representations for boosted embedding performance.
Improving Deep Learning Projections by Neighborhood Analysis
TLDR
The parameter space of this neural network approach is explained and a new neighborhood-based learning paradigm is proposed, which further improves the quality of the projections learned by the neural networks, and the approach is illustrated on large real-world datasets.
Spherical Rotation Dimension Reduction with Geometric Loss Functions
TLDR
This work has pointed out that this method is a specific incarnation of a grander idea of using a geometrically induced loss function in dimension reduction tasks and results relative to state-of-the-art competitors show considerable gains in ability to accurately approximate the subspace with fewer components and better structural preserving.
...
...

References

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction
TLDR
The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance.