Search bioRxiv⌕ Search
Home/Archive/bioRxiv

bioRxiv · 10.1101/2025.11.11.687920

MaxGeomHash: An Algorithm for Variable-Size Random Sampling of Distinct Elements

Hera, M. R.·Koslicki, D.·Martinez, C.
View original source ↗Export metadata ↓

Abstract

With the surge in sequencing data generated from an ever-expanding range of biological studies, designing scalable computational techniques has become essential. One effective strategy to enable large-scale computation is to split long DNA or protein sequences into k-mers, and summarize large k-mer sets into compact random samples (a.k.a. sketches). These random samples allow for rapid estimation of similarity metrics such as Jaccard or cosine, and thus facilitate scalable computations such as fast similarity search, classification, and clustering. Popular sketching tools in bioinformatics include Mash and sourmash. Mash uses the MinHash algorithm to generate fixed-size sketches; while sourmash employs FracMinHash, which produces sketches whose size scales linearly with the total number of k-mers. Here, we introduce a novel sketching algorithm, MO_SCPLOWAXC_SCPLOWGO_SCPLOWEOMC_SCPLOWHO_SCPLOWASHC_SCPLOW, which for a specified integer parameter b [≥] 1, will produce, without prior knowledge of n (the number of k-mers) a random sample of size b lg(n/b) + [O](b). Notably, this is the first permutation-invariant and parallelizable sketching algorithm to date that can produce sub-linear sketches, to the best of our knowledge. We also introduce a variant, -MO_SCPLOWAXC_SCPLOWGO_SCPLOWEOMC_SCPLOWHO_SCPLOWASHC_SCPLOW, that produces sketches of size{Theta} (n) for a given [isin] (0, 1). We study the algorithms properties, analyze generated sample sizes, verify theoretical results empirically, provide a fast implementation, and investigate similarity estimate quality. With intermediate-sized samples between constant (MinHash) and linear (FracMinHash), MO_SCPLOWAXC_SCPLOWGO_SCPLOWEOMC_SCPLOWHO_SCPLOWASHC_SCPLOW balances efficiency (smaller samples need less storage and processing) with accuracy (larger samples yield better estimates). On genomic datasets, we demonstrate that MO_SCPLOWAXC_SCPLOWGO_SCPLOWEOMC_SCPLOWHO_SCPLOWASHC_SCPLOW sketches can be used to compute a similarity tree (proxy for a phylogenetic tree) more accurately than MinHash, and more efficiently than FracMinHash. Our C++ implementation is available at: github.com/mahmudhera/kmer-sketch. Code to reproduce the analyses and experiments is at: github.com/KoslickiLab/MaxGeomHash.

Explore related subjects

bioinformaticsPreprint

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hera, M. R., Koslicki, D., Martinez, C.. 2025-11-13. MaxGeomHash: An Algorithm for Variable-Size Random Sampling of Distinct Elements. https://doi.org/10.1101/2025.11.11.687920

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2026

spatialMET: an open and scalable framework for spatial metabolomics analysis

Mass spectrometry imaging (MSI) enables spatially resolved metabolomics in intact tissue sections, but analysis remains challenging at scale. Existing MSI workflows often require users to combine multiple software tools, while others rely on proprietary vendor software that limits interoperability and reproducibility. To address these challenges, we developed spatialMET, an open-source framework that provides an end-to-end workflow for MSI analysis. spatialMET provides a unified platform for preprocessing, spatial domain detection, and visualization. Downstream analyses include differential abundance testing, spatial autocorrelation and gradient analysis, dimensionality reduction, and correlation network analysis. Spatial domain detection uses hcdist, a C-based hierarchical clustering implementation that substantially reduces runtime and memory use relative to existing R-based approaches. spatialMET can be run through an interactive R Shiny application or as a standalone command-line workflow for larger datasets or high-performance computing environments. Applied to mouse small cell lung cancer MALDI-MSI data containing 284,673 pixels, spatialMET identified tumor-associated, stromal, and adjacent lung spatial domains that aligned with matched histology. Differential abundance analysis identified 117 m/z features that differed between tumor and stromal regions, while spatial autocorrelation analyses revealed spatially structured abundance patterns. Applying spatialMET to mouse lung adenocarcinoma data from an entire lung lobe containing 338,477 pixels further demonstrated scalability and captured spatial heterogeneity across tumor and surrounding lung tissue. In summary, spatialMET provides a scalable, open-source framework for end-to-end spatial metabolomics analysis, and it is distributed as a Docker container for reproducible deployment. Source code and installation instructions are available at https://github.com/biodatalab/spatialMET.

bioinformatics↗
bioRxiv2026

Probing the transcriptome response to shivering in skeletal muscle using a multilayered bioinformatics approach

Cold acclimation holds therapeutic potential for improving metabolic health. We previously demonstrated that repeated cold-induced shivering enhances insulin sensitivity in humans. However, the molecular pathways that underlie the skeletal muscle shivering response, and how these relate to beneficial physiological effects, remain poorly understood. In this study, we combined complementary bioinformatics approaches to allow in-depth analysis of the transcriptomic response of human skeletal muscle to repeated shivering. We identified a robust transcriptional signature and show a sex-specific component in the shivering skeletal muscle response, which seemed to diminish following cold adaptation. Our findings provide mechanistic insights into cold-induced muscle adaptations, shed light on potential interesting molecular targets for further investigation, and emphasize the importance of including both sexes in future cold acclimation studies.

bioinformatics↗
bioRxiv2026

An Information Geometry approach to model topological trajectories and Gene Expression Radius from UMAP geometry.

Understanding the relationship between gene expression dynamics and cellular identity remains a central challenge in single cell biology. Here, we introduce a novel computational and mathematical framework that integrates information geometry, fuzzy topology, and UMAP analysis to model gene expression landscapes derived from single cell RNA sequencing data. We formalize gene expression data as a fuzzy topological space, where interactions between expression points are governed by probabilistic distributions inspired by manifold learning approaches such as UMAP. Within this framework, we define an information geometric structure through a Fisher metric induced by these distributions, enabling the computation of geodesic trajectories that capture cellular differentiation processes. A key contribution of this work is the derivation of analytical conditions, expressed as expression radius formulas, that characterize local neighborhoods in gene expression space. These conditions allow for the identification of genes associated with stem cell states and predictions in transitional cell types in future work. Application of the proposed framework to single cell datasets reveals biologically meaningful gene sets enriched in key regulatory pathways and transcription factors, demonstrating the capacity of our approach to uncover latent structure in complex gene expression data. Our results suggest that integrating differential geometry with statistical learning theory offers a powerful paradigm for modeling genotype and phenotype relationships and cellular state transitions, with potential implications for precision medicine and systems biology.

bioinformatics↗