Analyzing spatial omics data with varifold-based distances: dimensionality Reduction and multimodal Data Integration

Advances in spatial omics sequencing now enable acquisition of massive subcellular-scale datasets (millions of reads with hundreds of detectable genes). However, heterogeneity in measured features, spatial resolution, and physical sampling scope across technologies and experimental protocols introduces significant challenges for integrating these datasets within reference coordinate systems and across biological scales.

In this presentation, I will describe a set of technologies implemented in the xIV-LDDMM Toolkit Python package [2], developed for mapping data across scales and modalities as, for instance, aligning gene-level measurements to 2D or 3D tissue structures. I will first introduce the varifold-based distance and deformation framework, which enables comparison of diverse data types in spatial omics [1]. I will then focus on dimensionality-reduction strategies (both spatial and gene-wise) designed to reduce the computational burden of these large datasets: (i) an explicit censored-data representation for partial matching, enabling registration of whole brains to sparsely sampled subvolumes; (ii) a multiscale, scale-space optimization method for generating resampling grids that efficiently capture spatial geometry at fixed computational complexity; and (iii) mutual-information-based functional feature selection.