Unsupervised graph alignment finds the node correspondence between a pair of attributed graphs by only exploiting graph structure and node features. One category of recent studies first computes the node representation and then matches nodes with the largest embedding-based similarity, while the other category reduces the problem to optimal transport (OT) via Gromov-Wasserstein learning. However, it remains largely unexplored in the model expressiveness, as well as how theoretical expressivity impacts prediction accuracy. We investigate the model expressiveness from two aspects. First, we characterize the model'sdiscriminative powerin distinguishing matched and unmatched node pairs across two graphs. Second, we study the model's capability of guaranteeingnode matching propertiessuch as one-to-one matching and mutual alignment. Motivated by our theoretical analysis, we put forward a hybrid approach namedCombAlignwith stronger expressive power. Specifically, we enable cross-dimensional feature interaction for OT-based learning and propose an embedding-based method inspired by the Weisfeiler-Lehman test. We also apply non-uniform marginals obtained from the embedding-based modules to OT as priors for more expressiveness. Based on that, we propose a traditional algorithm-based refinement, which combines our OT and embedding-based predictions using the ensemble learning strategy and reduces the problem to maximum weight matching. With carefully designed edge weights, we ensure these matching properties and further enhance prediction accuracy. By extensive experiments, we demonstrate a significant improvement of 14.5% in alignment accuracy compared to state-of-the-art approaches and confirm the soundness of our theoretical analysis.

Single-cell technologies have enabled the high-dimensional characterization of cell populations at an unprecedented scale. The innate complexity and increasing volume of data pose significant computational and analytical challenges, especially in comparative studies delineating cellular architectures across various biological conditions (i.e. generation of sample-level distance matrices). Optimal Transport is a mathematical tool that captures the intrinsic structure of data geometrically and has been applied to many bioinformatics tasks. In this paper, we propose QOT (Quantized Optimal Transport), a new method enabling efficient computation of sample-level distance matrix from large-scale single-cell omics data through a quantization step. We apply our algorithm to real-world single-cell genomics and pathomics datasets, aiming to extrapolate cell-level insights to inform sample-level categorizations. Our empirical study shows that QOT outperforms existing two OT-based algorithms in accuracy and robustness when obtaining a distance matrix from high throughput single-cell measures at the sample level. Moreover, the sample level distance matrix could be used in the downstream analysis (i.e. uncover the trajectory of disease progression), highlighting its usage in biomedical informatics and data science.

The knowledge of the anatomical shape of both gross and microscopic structures is the key to understanding the effects of disease processes on cellular structure. Geometric morphometric methods, such as Procrustes superimposition, and Spherical Harmonics (SPHARM), have been used to capture the biological shape variation and group differences in morphology. Previous SPHARM-MAT techniques use the CALD algorithm to parameterize the mesh surface. It starts from initial mapping and performs local and global smoothing methods alternately to control the area and length distortions simultaneously. However, this parameterization may not be sufficient in complex morphological cases. To bridge this gap, we propose SPHARM-OT, an enhanced SPHARM surface modeling method using optimal transport (OT) for spherical parameterization. First, the genus 0 3D objects are conformally mapped onto a sphere. Then the optimal transport theory via spherical power diagram is introduced to minimize the area distortion. This new algorithm can effectively reduce the area distortion and lead to a better reconstruction result. We demonstrate the effectiveness of the method by applying it to the human sphenoidal paranasal sinuses.

Popular semi-supervised image segmentation networks suf-fer from two problems: firstly, supervision is only performed on the last layer of the decoder, resulting in the network's weak generalization ability; secondly, the geometry shape constraints of targets are frequently disregarded in these net-works, leading to poor segmentation results. To address these issues, we propose a novel shape-guided dual consistency semi-supervised learning framework for 3D medical image segmentation. The proposed framework makes two contri-butions. Initially, we introduce a shape constraint to learn the shape representation, which converts the difference be-tween two networks into an unsupervised loss and lets the model learn the boundary information of targets. Addition-ally, we develop a deep-supervised knowledge transfer strat-egy that improves the generalization ability of the network without increasing extra computation costs. Experiments demonstrate that the proposed framework outperforms state-of-the-art semi-supervised methods due to the strong ability of knowledge mining on unlabeled data.