[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81533-en":3,"doc-seo-81533-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},81533,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782698725881665579",8,"Research & Report","Uncovering Smooth Structures in Single-Cell Data with PCS-Guided Neighbor Embeddings","Single-cell sequencing enables detailed study of cell-state transitions, yet extracting smooth, low-dimensional structure from noisy, high-dimensional data remains difficult. Neighbor embedding methods like t-SNE and UMAP are widely used but can distort results, leading to misleading interpretations. This work evaluates NE algorithms using the Predictability–Computability–Stability (PCS) framework, identifies artifacts and instability, and introduces NESS to produce interpretable, stable embeddings. NESS leverages stability metrics and efficient workflows to recover developmental trajectories across diverse datasets and enables robust inference of transitional and stable cell states.","arXiv :2506 .22228v2 [ stat .ML] 10 Jul 2026  \nUncovering smooth structures in single-cell data with PCS-guided  \nneighbor embeddings  \nRong Ma*,†1,2,3, Xi Li*1 , Jingyuan Hu 1 , and Bin Yu†4,5,6  \n1 Department of Biostatistics, Harvard T.H. Chan School of Public Health  \n2 Department of Data Science, Dana-Farber Cancer Institute  \n3 Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard  \n4 Department of Statistics, University of California, Berkeley  \n5 Department of EECS, University of California, Berkeley  \n6 Center for Computational Biology, University of California, Berkeley  \nAbstract  \nSingle-cell sequencing is revolutionizing biology by enabling detailed investigations of cellstate transitions. Many biological processes unfold along continuous trajectories, yet it remains challenging to extract smooth, low-dimensional representations from inherently noisy, highdimensional single-cell data. Neighbor embedding (NE) algorithms, such as t-SNE and UMAP, are widely used to embed high-dimensional single-cell data into low dimensions. But they often introduce undesirable distortions, resulting in misleading interpretations. Existing evaluation methods for NE algorithms primarily focus on separating discrete cell types rather than capturing continuous cell-state transitions, while dynamic modeling approaches rely on strong assumptions about cellular processes and specialized data. To address these challenges, we build on the Predictability–Computability–Stability (PCS) framework for reliable and reproducible data-driven discoveries. First, we systematically evaluate popular NE algorithms through empirical analysis, simulation, and theory, and reveal their key shortcomings such as artifacts and instability. We then introduce NESS, a principled and interpretable machine learning approach to improve NE representations by leveraging algorithmic stability and to enable robust inference of smooth biological structures. NESS offers useful concepts, quantitative stability metrics, and efficient computational workflows to uncover developmental trajectories and cell-state transitions in single-cell data. Finally, we apply NESS to multiple single-cell datasets, including those about pluripotent stem cell differentiation, organoid development, and multiple tissue-specific lineage trajectories. Across these diverse contexts, NESS consistently yields useful and verifiable biological insights, such as identification of transitional and stable cell states and quantification of transcriptional dynamics during development. Notably, NESS resolves distinct neuronal subpopulations during embryoid formation and provides a deeper understanding of their cell-state dynamics.  \n1 Introduction  \nSingle-cell sequencing technologies generate high-dimensional molecular profiles at cellular resolution, enabling the study of cell-state transitions in processes such as differentiation, reprogram-  \n∗ These authors contributed equally †Corresponding authors  \nming, and disease progression [83, 71 , 64 , 20 , 62 , 74 , 25] . While these datasets are often sparse and noisy due to technical factors such as dropout events and measurement variability, the cellular states they capture typically arise from structured, continuous biological processes. Consequently, large-scale single-cell datasets frequently exhibit lower-dimensional smooth manifold structures embedded within the high-dimensional feature space. These manifolds reflect the geometry of the underlying biological dynamics and can take the form of linear trajectories [62, 29], cycles [46], or branching tree-like structures [35, 73] . Identifying and characterizing such geometric structures is essential for understanding lineage relationships, developmental pathways, and disease progression [83, 71 , 64 , 20] . In particular, trajectory inference methods aim to organize cells along a continuous trajectory in a lower-dimensional space, capturing the progression of biological processes [62, 74 , 25","cbCaicVpyA1NTs0L","https://ap.wps.com/l/cbCaicVpyA1NTs0L","pdf",13628298,1,62,"English","en",105,"# Introduction\n## Single-cell manifold structures\n## Neighbor embedding methods and applications\n## Reliability challenges and artifacts","[{\"question\":\"Why are neighbor embedding (NE) methods like t-SNE and UMAP difficult to trust for single-cell trajectories?\",\"answer\":\"The document explains that NE methods can introduce substantial artifacts and distortions, especially with noisy, high-dimensional single-cell data, which can misrepresent underlying smooth biological structures and transitions.\"},{\"question\":\"How does the PCS framework contribute to evaluating NE algorithms?\",\"answer\":\"The work uses the Predictability–Computability–Stability (PCS) framework to systematically evaluate popular NE algorithms through empirical analysis, simulation, and theory, revealing shortcomings such as artifacts and instability.\"},{\"question\":\"What is NESS, and how does it improve NE representations?\",\"answer\":\"NESS is an interpretable machine learning approach that improves embeddings by leveraging algorithmic stability, providing quantitative stability metrics and efficient computational workflows to uncover smooth biological structures and enable robust 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are neighbor embedding (NE) methods like t-SNE and UMAP difficult to trust for single-cell trajectories?","Question",{"text":74,"@type":75},"The document explains that NE methods can introduce substantial artifacts and distortions, especially with noisy, high-dimensional single-cell data, which can misrepresent underlying smooth biological structures and transitions.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the PCS framework contribute to evaluating NE algorithms?",{"text":79,"@type":75},"The work uses the Predictability–Computability–Stability (PCS) framework to systematically evaluate popular NE algorithms through empirical analysis, simulation, and theory, revealing shortcomings such as artifacts and instability.",{"name":81,"@type":72,"acceptedAnswer":82},"What is NESS, and how does it improve NE representations?",{"text":83,"@type":75},"NESS is an interpretable machine learning approach that improves embeddings by leveraging algorithmic stability, providing 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