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Graph matching is a fundamental tool in computer vision and pattern recognition. In this paper, we introduce an algorithm for graph matching based on the proximal operator, referred to as differentiable proximal graph matching (DPGM).…
Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting…
Model-based clustering is widely used for identifying and distinguishing types of diseases. However, modern biomedical data coming with high dimensions make it challenging to perform the model estimation in traditional cluster analysis. The…
Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…
Background: It is well known that the development of cancer is caused by the accumulation of somatic mutations within the genome. For oncogenes specifically, current research suggests that there is a small set of "driver" mutations that are…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
Graph neural networks (GNNs) have been used extensively for addressing problems in drug design and discovery. Both ligand and target molecules are represented as graphs with node and edge features encoding information about atomic elements…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
Gene expression data is widely used in disease analysis and cancer diagnosis. However, since gene expression data could contain thousands of genes simultaneously, successful microarray classification is rather difficult. Feature selection…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
Magnetic Resonance Spectroscopy (MRS) provides valuable information to help with the identification and understanding of brain tumors, yet MRS is not a widely available medical imaging modality. Aiming to counter this issue, this research…
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…
Superpixel segmentation algorithms are to partition an image into perceptually coherence atomic regions by assigning every pixel a superpixel label. Those algorithms have been wildly used as a preprocessing step in computer vision works, as…
Graph neural networks (GNNs) are increasingly used to model biological systems, yet the reliability of post-hoc explanation methods for recovering meaningful molecular mechanisms remains unclear. Here, we systematically evaluate four widely…
We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…
The Mapper algorithm from topological data analysis constructs a graph summarizing the shape of a high-dimensional dataset, and groups of data points identified within this graph are widely interpreted as evidence of distinct subtypes.…
The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless developments of computer architectures and algorithms. This explosion in the number and extent (in size and time) of MD…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…
Motivation: Tumor classification using Imaging Mass Spectrometry (IMS) data has a high potential for future applications in pathology. Due to the complexity and size of the data, automated feature extraction and classification steps are…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…