DMT-Dens: Density-preserving manifold visualization for biological data

Motivation: Low-dimensional embeddings are widely used to explore cell-state heterogeneity in single-cell and other high-dimensional biological data. Although many methods preserve local neighborhoods, they may distort the apparent sampling density of processed observations, altering the visual contrast between dense and sparse regions and complicating the interpretation of rare, transitional, or continuous cell-state populations. Results: We present DMT-Dens, a parametric manifold-visualization method built on a latent-token Transformer encoder. The model integrates rank-based manifold alignment with hard-pair aggregation. To preserve density, it optimizes a loss based on the Pearson correlation between k-nearest-neighbor log-radius estimates in the processed input and two-dimensional embedding spaces. Benchmark evaluations demonstrate strong density preservation, particularly on biological datasets, while retaining competitive label separability. Availability: Source code, data-processing scripts, and resolved experiment configurations are available at https://github.com/Ruizhe-wang/DMT-Dens.

Transfer Learning in High-Dimensional Clustering: Minimax Thresholds and Applications in Single-Cell Data

Clustering is a fundamental problem in statistics, with applications across many scientific disciplines. In many modern applications involving clustering, the primary dataset (the target data) is accompanied by related datasets (the source data). Transferring information from such sources may improve clustering accuracy in the target, making transfer learning for clustering practically important. Despite recent progress, the conditions under which source data improve target clustering remain unclear in high-dimensional settings, even for the canonical Gaussian mixture model. In this paper, we study the clustering problem in a two-community Gaussian mixture model where relatedness is captured by the geometric alignment of the target and source cluster means. We develop a minimax-optimal transfer-assisted clustering procedure and characterize, up to logarithmic factors, the phase transition for consistent target clustering in terms of the signal-to-noise ratios, sample sizes, ambient dimension, and degree of alignment between the datasets. The technique is also extended to adaptively choose between the target-only or the source assisted clustering depending on the target signal strength. Furthermore, we also extend our techniques to accommodate multiple communities and and multiple source datasets. Extensive simulations and an analysis of a human lung single-cell RNA-sequencing atlas demonstrate the practical effectiveness of our methods.

Making Single-Cell Data Distillation Auditable: Traceable Real-Cell Coresets via Discrete Min--Max Selection

Large single-cell datasets are expensive to store, curate, and repeatedly reuse for model training. Data distillation can reduce this burden by building smaller training sets. However, many existing methods rely on synthetic cells. These synthetic cells do not retain direct correspondence with assayed cells and genes. This limits source-level inspection and biological traceability. Moreover, real-cell expression matrices are often sparse and noisy. In light of these challenges, we propose Minmax-CF, a label-aware characteristic-function selector for traceable single-cell data distillation. Minmax-CF formulates compression as a discrete min--max selection problem over characteristic-function directions. It uses entropy-regularized maximization to emphasize the least preserved directions. Greedy minimization ranks cells and genes by how much they reduce the resulting weighted error. The method alternates cell and gene selection under explicit axis-specific budgets. Across five coarse-lineage benchmarks and five compression budgets, Minmax-CF retains 95.3% of the Full-reference macro-F1 on average, with gaps that exceed one per-seed standard deviation. It also retains exact source-cell indices and original gene symbols. Compared with size-matched synthetic PCA-Centroid and Distribution Matching (DM) baselines, Minmax-CF achieves higher coarse-lineage macro-F1 in 24 of 25 comparisons against each baseline. It exceeds their average performance by 10.4% and 17.4%, respectively. Retained cells can also be projected onto independently computed embeddings for direct biological interpretation.

Privacy-preserving federated tensor decomposition of single-cell immune data: recovering multicellular programs across institutions

Tensor decomposition of donor $\times$ cell-type $\times$ gene single-cell data recovers \emph{multicellular programs}: coordinated axes of inter-individual transcriptional variation that span cell types and stratify disease. Yet immune single-cell atlases are increasingly multi-institution, multi-ancestry, and governed, so patient cells often cannot be pooled. We present a federated estimator: each site computes a local program subspace, and a coordinator merges these by stacked SVD under federated global-mean centering, provably equivalent (up to truncation) to the centralised decomposition. This centering makes the merge robust to site-label confounding (program AUC $0.957$ vs.\ $0.861$ for naive per-site centering). Only program subspaces leave a site, and aggregation is compatible with secure aggregation. On a 261-donor systemic lupus erythematosus atlas it recovers the canonical interferon program (ISG enrichment AUC $0.998$; case--control separation $0.958$; bootstrap $Δ\text{AUC}=-0.000$, 95\% CI $[-0.004,+0.012]$ vs.\ centralised), across institution-scale and multi-ancestry partitions, and across three \emph{real} COVID-19 sites (subspace correlation $0.989$). It recovers the program when \emph{no site observes all cell types} (correlation $1.000$, exact by construction), which fixed-feature federated PCA cannot. On an interstitial-lung-disease atlas the recovered program predicts disease better than the best single cell type (AUC $0.96$ vs.\ $0.91$; gap 95\% CI excludes zero) and the advantage survives federation; a liver cohort is consistent ($p=0.005$). Membership-inference shows secure aggregation cuts attack AUC from $0.91$ to $0.61$. The method enables cross-institution, cross-ancestry recovery of multicellular immune programs without sharing cells.