Differential rank preservation manifold learning

Authors: Henry Han , Luyu Niu , Diane Li , Jiacun Wang

View a PDF of the paper titled Differential rank preservation manifold learning, by Henry Han and 3 other authors

View PDF

HTML (experimental)

Abstract: Manifold learning methods like t-SNE and UMAP preserve local neighborhoods, but they do not preserve the ranking of the neighbors inside them. Two embeddings can return the same neighbor set while disagreeing on which point is closest. This loss of order degrades downstream applications that value the order in the embedding. We propose Smooth Rank t-SNE (SR-tSNE), which adds a differentiable rank term to the standard t-SNE loss. To enable efficient training, this term uses a sigmoid rank approximation to explicitly force a point's true high-dimensional neighbors to outrank unrelated intruders and retain their original order. We also introduce Ordinal DLP (O-DLP), an extension of the Degree of Locality Preservation (DLP) metric that credits a neighbor only when it returns at its original rank. Across eight benchmarks spanning image, text, speech, remote-sensing and single-cell data, SR-tSNE outperforms 12 baselines in rank preservation and neighborhood overlap. Ablation studies demonstrate our rank term alone boosts O-DLP by 5% to 28%, a gain not achievable using standard pairwise loss. This advantage transfers to downstream applications. SR-tSNE achieves the best label-transfer performance across seven vision datasets. For cell-type discovery across six single-cell datasets, it ranks first in 17 of 18 dataset-metric combinations, whether clustering resolution is selected with or without cell-type labels. In intraday trading, SR-tSNE achieves higher returns, lower risk, and lower turnover than the baselines. To our knowledge, SR-tSNE is the first t-SNE-family method with explicit order preservation.

Comments:

67 pages, 10 figures, 28 tables

Subjects:

Artificial Intelligence (cs.AI) ; Machine Learning (cs.LG)

Cite as:

arXiv:2610.41107 [cs.AI]

(or

arXiv:2610.41107v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.41107

Focus to learn more

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Henry Han [ view email ]

[v1]

Fri, 30 Oct 2026 00:56:05 UTC (11,745 KB)

Full-text links:

Access Paper:

View a PDF of the paper titled Differential rank preservation manifold learning, by Henry Han and 3 other authors

View PDF

HTML (experimental)

TeX Source

view license

Additional Features

Audio Summary

Current browse context:

cs.AI

< prev

next >

new

recent

| 2026-10

Change to browse by:

cs

cs.LG

References & Citations

SciX

Google Scholar

Semantic Scholar

export BibTeX citation

Loading...

BibTeX formatted citation

loading...

Data provided by:

Bookmark

Bibliographic Tools

Bibliographic and Citation Tools

Bibliographic Explorer Toggle

Bibliographic Explorer ( What is the Explorer? )

Connected Papers Toggle

Connected Papers ( What is Connected Papers? )

Litmaps Toggle

Litmaps ( What is Litmaps? )

scite.ai Toggle

scite Smart Citations ( What are Smart Citations? )

Code, Data, Media

Code, Data and Media Associated with this Article

alphaXiv Toggle

alphaXiv ( What is alphaXiv? )

Links to Code Toggle

CatalyzeX Code Finder for Papers ( What is CatalyzeX? )

DagsHub Toggle

DagsHub ( What is DagsHub? )

GotitPub Toggle

Gotit.pub ( What is GotitPub? )

Huggingface Toggle

Hugging Face ( What is Huggingface? )

ScienceCast Toggle

ScienceCast ( What is ScienceCast? )

Demos

Demos

Replicate Toggle

Replicate ( What is Replicate? )

Spaces Toggle

Hugging Face Spaces ( What is Spaces? )

Spaces Toggle

TXYZ.AI ( What is TXYZ.AI? )

Related Papers

Recommenders and Search Tools

Link to Influence Flower

Influence Flower ( What are Influence Flowers? )

Core recommender toggle

CORE Recommender ( What is CORE? )

Author

Venue

Institution

Topic

About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Which authors of this paper are endorsers? |

Disable MathJax ( What is MathJax? )