Related papers: Multiparameter Persistent Homology for Molecular P…
Recently, the study of graph neural network (GNN) has attracted much attention and achieved promising performance in molecular property prediction. Most GNNs for molecular property prediction are proposed based on the idea of learning the…
Molecular fingerprints, i.e. feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of potential energy surface and interatomic force. In this paper, we…
Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…
We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…
A molecule is a complex of heterogeneous components, and the spatial arrangements of these components determine the whole molecular properties and characteristics. With the advent of deep learning in computational chemistry, several studies…
Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…
Weighted digraphs are used to model a variety of natural systems and can exhibit interesting structure across a range of scales. In order to understand and compare these systems, we require stable, interpretable, multiscale descriptors. To…
Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as…
Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at distance. In this paper, we present a persistent homology-based method to extract topological features (the so-called…
In drug-discovery-related tasks such as virtual screening, machine learning is emerging as a promising way to predict molecular properties. Conventionally, molecular fingerprints (numerical representations of molecules) are calculated…
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
Techniques from topological data analysis (TDA) have proven effective in studying time-dependent data arising in dynamic systems, such as animal swarming behavior and spatiotemporal patterns in neuroscience. While early algorithms leveraged…
Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…
Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates,…
Identifying molecular signatures from complex disease patients with underlying symptomatic similarities is a significant challenge in the analysis of high dimensional multi-omics data. Topological data analysis (TDA) provides a way of…
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
Persistent homology is a relatively new tool often used for \emph{qualitative} analysis of intrinsic topological features in images and data originated from scientific and engineering applications. In this paper, we report novel…
Magnetic Resonance Fingerprinting (MRF) enables the simultaneous quantification of multiple properties of biological tissues. It relies on a pseudo-random acquisition and the matching of acquired signal evolutions to a precomputed…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…