Harmonic Alignment

TL;DR

Harmonic Alignment introduces a geometry-based framework for aligning and fusing datasets from different modalities or batches without requiring pointwise correspondence, using harmonic expansions of data features derived from diffusion operators.

Contribution

The paper presents a novel harmonic alignment method that leverages diffusion geometry and partial feature correspondence to align datasets without pointwise matching, improving data fusion and batch effect correction.

Findings

Effective in biological data fusion, including scRNA-seq and scATAC-seq

Successfully removes batch effects between biological samples

Demonstrates robustness across multiple datasets

Abstract

We propose a novel framework for combining datasets via alignment of their intrinsic geometry. This alignment can be used to fuse data originating from disparate modalities, or to correct batch effects while preserving intrinsic data structure. Importantly, we do not assume any pointwise correspondence between datasets, but instead rely on correspondence between a (possibly unknown) subset of data features. We leverage this assumption to construct an isometric alignment between the data. This alignment is obtained by relating the expansion of data features in harmonics derived from diffusion operators defined over each dataset. These expansions encode each feature as a function of the data geometry. We use this to relate the diffusion coordinates of each dataset through our assumption of partial feature correspondence. Then, a unified diffusion geometry is constructed over the aligned data, which can also be used to correct the original data measurements. We demonstrate our method on several datasets, showing in particular its effectiveness in biological applications including fusion of single-cell RNA sequencing (scRNA-seq) and single-cell ATAC sequencing (scATAC-seq) data measured on the same population of cells, and removal of batch effect between biological samples.