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

Given dense image feature correspondences of a non-rigidly moving object across multiple frames, this paper proposes an algorithm to estimate its 3D shape for each frame. To solve this problem accurately, the recent state-of-the-art…

Single-cell RNA sequencing (scRNA-seq) enables single-cell transcriptomic profiling, revealing cellular heterogeneity and rare populations. Recent deep learning models like Geneformer and Mouse-Geneformer perform well on tasks such as…

The input data features set for many data driven tasks is high-dimensional while the intrinsic dimension of the data is low. Data analysis methods aim to uncover the underlying low dimensional structure imposed by the low dimensional hidden…

Understanding low-dimensional structures within high-dimensional data is crucial for visualization, interpretation, and denoising in complex datasets. Despite the advancements in manifold learning techniques, key challenges-such as limited…

Cell type identification from single-cell transcriptomic data is a common goal of single-cell RNA sequencing (scRNAseq) data analysis. Neural networks have been employed to identify cell types from scRNAseq data with high performance.…

Graph neural networks (GNNs) face significant challenges with class imbalance, leading to biased inference results. To address this issue in heterogeneous graphs, we propose a novel framework that combines Graph Neural Network (GNN) and…

Multimodal data provide complementary information of a natural phenomenon by integrating data from various domains with very different statistical properties. Capturing the intra-modality and cross-modality information of multimodal data is…

DNA microarray gene-expression data has been widely used to identify cancerous gene signatures. Microarray can increase the accuracy of cancer diagnosis and prognosis. However, analyzing the large amount of gene expression data from…

Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Non-negative Matrix…

Over the past decades, the increasing dimensionality of data has increased the need for effective data decomposition methods. Existing approaches, however, often rely on linear models or lack sufficient interpretability or flexibility. To…

Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled…

Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…

In this paper, we explore a volume-based stable embedding of multi-dimensional signals based on Grassmann manifold, via Gaussian random measurement matrices. The Grassmann manifold is a topological space in which each point is a linear…

Single-cell sequencing is revolutionizing biology by enabling detailed investigations of cell-state transitions. Many biological processes unfold along continuous trajectories, yet it remains challenging to extract smooth, low-dimensional…

This paper looks into the problem of handling imbalanced data in a multi-label classification problem. The problem is solved by proposing two novel methods that primarily exploit the geometric relationship between the feature vectors. The…

Single-cell RNA sequencing (scRNA-seq) is essential for unraveling cellular heterogeneity and diversity, offering invaluable insights for bioinformatics advancements. Despite its potential, traditional clustering methods in scRNA-seq data…

3D cell segmentation methods are often hindered by \emph{oversegmentation}, where a single cell is incorrectly split into multiple fragments. This degrades the final segmentation quality and is notoriously difficult to resolve, as…

Single-cell RNA sequencing (scRNA-seq) data exhibit strong and reproducible statistical structure. This has motivated the development of large-scale foundation models, such as TranscriptFormer, that use transformer-based architectures to…

Single-cell RNA sequencing (scRNA-seq) profiles large numbers of cells but loses spatial context, whereas spatial transcriptomics (ST) preserves partial spatial structure at lower resolution. Most existing integration methods either…

In this paper, we propose a unified framework for sampling, clustering and embedding data points in semi-metric spaces. For a set of data points $\Omega=\{x_1, x_2, \ldots, x_n\}$ in a semi-metric space, we consider a complete graph with…