high-dimensional data embedding

High-dimensional data analysis faces fundamental challenges including empirically unjustified embedding method selection, poorly characterized performance bounds, and fragmented theoretical debates. This study systematically reviews mainstream dimensionality reduction techniques—including t-SNE, UMAP, PCA, and autoencoders—synthesizing scattered literature and key controversies to propose the first practice-oriented three-dimensional framework for low-dimensional embeddings: “generation–evaluation–application.” We conduct a comprehensive empirical evaluation across diverse real-world datasets and downstream tasks, rigorously characterizing each algorithm’s trade-offs in preserving local versus global structure, robustness to noise and hyperparameter variation, and interpretability. Our analysis establishes clear applicability boundaries and inherent limitations for each method. The resulting best-practice guidelines integrate theoretical rigor with engineering feasibility, providing the field with standardized evaluation protocols and principled criteria for method selection. (149 words)

This work addresses the limited interpretability and poor cross-batch robustness of high-dimensional embeddings in single-cell sequencing data. We establish, for the first time, a theoretical correspondence between the geometric structure of language model (LLM) token embeddings and the single-cell expression space, proposing a novel “geometry-driven cell embedding” paradigm. Methodologically, we treat cells as tokens and leverage LLM embedding analysis, interpretability probing, in-context reasoning, and manifold learning to model the low-dimensional geometric structure of cellular state space. Our contributions are threefold: (1) uncovering the regulatory role of manifold geometry in embedding robustness and interpretability; (2) constructing the first unified framework integrating LLM-based interpretability techniques with single-cell atlas construction; and (3) significantly improving generalizability and biological interpretability in cross-batch integration, cell-type annotation, and functional-state inference.

Biomedical high-dimensional data visualization is often hindered by insufficient tool security, scalability, and reproducibility. To address this, we propose a pure-browser, zero-local-computation visualization framework natively supporting heatmaps, PCA, and t-SNE—requiring no server deployment and thereby ensuring data privacy and cross-platform portability. Our method introduces novel integration of automatic R code generation to guarantee full analytical reproducibility; incorporates optimized dimensionality reduction algorithms and built-in CSV/TSV parsing with normalization, annotation, and interactive rendering capabilities—enabling millisecond-scale responsiveness and scalability to thousands of samples. The framework is openly distributed via dual channels: GitHub Pages for web access and a CRAN-hosted R package for programmatic use. It has been successfully deployed in multiple bioinformatics education and collaborative research settings.

Widespread misuse of dimensionality reduction techniques—such as inappropriate projection interpretation and algorithmic misselection—is prevalent across non-computing disciplines including biology, chemistry, physics, and business. Method: We conducted the first cross-disciplinary empirical study, combining bibliometric analysis of 21,249 publications with deep qualitative coding of 71 representative papers. Contribution/Results: We identify pronounced disciplinary algorithmic preferences (e.g., t-SNE dominance in biology vs. PCA prevalence in physics) and reveal that over 60% of studies exhibit critical interpretive flaws. We propose a novel “confirmatory + exploratory” hybrid workflow framework, systematically categorize recurrent misuse patterns, and provide eight actionable, cross-disciplinary best-practice guidelines. This work establishes a new normative paradigm for integrating rigorous scientific visualization with domain-specific research practice.

In high-dimensional data dimensionality reduction, the initial similarity graph is unreliable due to the “curse of dimensionality” and information sparsity, impeding cluster separation—especially as dataset size increases. To address this, we propose LocalMAP, a novel algorithm that introduces a dynamic local subgraph extraction and online update mechanism. LocalMAP achieves fine-grained, adaptive refinement of the adjacency graph via embedding-driven subgraph sampling, local neighborhood-aware adaptive reweighting, and iterative graph optimization. Compared with conventional methods (e.g., t-SNE, UMAP), LocalMAP significantly improves clustering structure recovery accuracy. On large-scale transcriptomic datasets, it successfully disentangles biologically meaningful but previously confounded subpopulations, accurately identifying critical cell types that were either missed or erroneously merged in prior analyses. LocalMAP thus establishes a new paradigm for interpretable, scalable dimensionality reduction of high-dimensional biological data.

Single-cell RNA sequencing data exhibit diverse geometric structures—such as clusters, trajectories, and branches—yet existing analytical methods often assume predefined shapes and lack the capacity to automatically infer the intrinsic geometry of the data. To address this limitation, this work introduces scShapeBench, the first comprehensive benchmark specifically designed for geometric structure identification in single-cell data, comprising both synthetic and expert-annotated real datasets. Furthermore, the authors propose scReebTower, a novel method grounded in diffusion geometry that automatically detects data shape by extracting Reeb graphs. By integrating diffusion geometry with topological skeleton sampling, scReebTower bridges the gap between visualization and the selection of downstream analysis pipelines. Experimental results demonstrate that scReebTower outperforms existing approaches such as PAGA and Mapper across multiple datasets, confirming its effectiveness in automated geometric structure recognition.

The absence of controllable, reproducible simulation benchmarks for complex high-dimensional structures—including linear/nonlinear dependencies, clustering, and anomalies—hinders rigorous evaluation of machine learning methods. Method: We introduce *cardinalR*, an open-source R package that unifies the generative modeling of diverse high-dimensional structures, including nonlinear manifolds and local anomalies. Its core methodology integrates piecewise polynomial and radial basis function representations to construct flexible nonlinear manifolds, while leveraging Gaussian/t-distribution mixtures to generate clusters and anomalies. All structural properties—including dimensionality, signal-to-noise ratio, and structural strength—are fully parameterized and tunable. Contribution/Results: *cardinalR* provides a standardized, extensible benchmark framework for evaluating dimensionality reduction (e.g., t-SNE, UMAP) and supervised/unsupervised learning algorithms. It significantly enhances model interpretability validation and is accompanied by curated benchmark datasets and comprehensive usage examples.

Nonlinear dimensionality reduction of high-dimensional data often yields spurious clustering structures under noise, leading to erroneous interpretations—necessitating reliable diagnostic tools. This paper proposes a multi-view visual diagnostic framework that jointly evaluates local and global structure preservation, quantifies dimensionality reduction stability via resampling, and assesses clustering consistency across projections. The framework enables interactive artifact identification. Built upon it, we develop DRtool—an open-source R package integrating state-of-the-art algorithms (e.g., t-SNE, UMAP) and diagnostic visualizations, including neighborhood preservation heatmaps, resampling consistency curves, and projection confidence ellipses. These features substantially enhance the interpretability and reliability of clustering outcomes. Extensive experiments demonstrate that our method effectively distinguishes biologically meaningful signals from algorithmic artifacts, with robust performance validated on real-world single-cell transcriptomic datasets.

Current cell state discovery relies on dimensionality reduction, visualization, and manual clustering interpretation; however, intra-cluster heterogeneity frequently compromises biomarker identification accuracy, resulting in high trial-and-error costs and poor interpretability. To address this, we propose a novel framework integrating Mixture-of-Experts (MoE) modeling with interactive visual analytics: the MoE model automatically learns nonlinear associations between cell subpopulations and gene biomarkers without imposing rigid clustering assumptions; concurrently, the visual interface enables biologists to iteratively formulate, test, and refine state hypotheses while incorporating domain knowledge to guide model optimization. Case studies on real single-cell datasets demonstrate that our approach significantly improves biomarker detection accuracy and biological interpretability, successfully aiding the discovery of novel cell states and reducing analytical uncertainty by 42% (per expert assessment) compared to conventional methods.

This study addresses the challenge of balancing local heterogeneity, robustness, and interpretability in single-cell RNA sequencing data analysis. It introduces persistent sheaf theory—a novel application in this domain—and proposes a multiscale embedding method based on the persistent sheaf Laplacian. By constructing dynamic sheaf structures over cellular neighborhoods, the approach tracks the evolution of local relationships across resolutions and aggregates spectral statistics to generate unsupervised cell representations without requiring additional training. Evaluated on twelve benchmark datasets, the method matches or outperforms existing state-of-the-art techniques, demonstrating strong empirical performance, generalization capability, and an interpretable characterization of multiscale topological structures.