Related papers: Multiscale Grassmann Manifolds for Single-Cell Dat…

Training model to generate data has increasingly attracted research attention and become important in modern world applications. We propose in this paper a new geometry-based optimization approach to address this problem. Orthogonal to…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the exponential parameter space of product manifolds of categorical distributions as a novel method…

Computational modeling of single-cell gene expression is crucial for understanding cellular processes, but generating realistic expression profiles remains a major challenge. This difficulty arises from the count nature of gene expression…

As single-cell gene expression data analysis continues to grow, the need for reliable clustering methods has become increasingly important. The prevalence of heuristic means for method choice could lead to inaccurate reports if…

In geosciences, the use of classical Euclidean methods is unsuitable for treating and analyzing some types of data, as this may not belong to a vector space. This is the case for correlation matrices, belonging to a subfamily of symmetric…

When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…

The paper is motivated from clustering problem in high-throughput mixed datasets. Clustering of such datasets can provide much insight into biological associations. An open problem in this context is to simultaneously cluster…

Scarcity of annotated data, particularly for rare or atypical morphologies, present significant challenges for cell and nuclei segmentation in computational pathology. While manual annotation is labor-intensive and costly, synthetic data…

Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or…

Self-supervised learning (SSL) has proven to be a powerful approach for extracting biologically meaningful representations from single-cell data. To advance our understanding of SSL methods applied to single-cell data, we present…

Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse and complex molecular and biomolecular datasets due to the limited…

Recent advances in technology have enabled the measurement of RNA levels for individual cells. Compared to traditional tissue-level bulk RNA-seq data, single cell sequencing yields valuable insights about gene expression profiles for…

This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds and incorporates the mini-batch strategy that is often used…

A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the…

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds…

The application of single-cell molecular profiling coupled with spatial technologies has enabled charting cellular heterogeneity in reference tissues and in disease. This new wave of molecular data has highlighted the expected diversity of…

Biological functions stem from coordinated interactions among proteins, nucleic acids and small molecules. Mass spectrometry technologies for reliable, high throughput single-cell proteomics will add a new modality to genomics and enable…

Applications of single-cell RNA sequencing in various biomedical research areas have been blooming. This new technology provides unprecedented opportunities to study disease heterogeneity at the cellular level. However, unique…

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…