相关论文: Persistent homology-based descriptor for machine-l…

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…

Persistent homology (PH) is a popular tool for topological data analysis that has found applications across diverse areas of research. It provides a rigorous method to compute robust topological features in discrete experimental…

Multiphoton photoreduction enables high-fidelity fabrication of complex 3D microstructures, yet reliable process-structure-property (PSP) prediction remains difficult because the available data are sparse, heterogeneous, and…

Persistent homology (PH) is one of the main methods used in Topological Data Analysis. An active area of research in the field is the study of appropriate notions of PH representatives, which allow to interpret the meaning of the…

Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a…

0-dimensional persistent homology is known, from a computational point of view, as the easy case. Indeed, given a list of $n$ edges in non-decreasing order of filtration value, one only needs a union-find data structure to keep track of the…

We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an…

Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics and transport is one of most challenging tasks in biological science. In the present work, persistent homology is,…

Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…

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…

It is difficult to quantify structure-property relationships and to identify structural features of complex materials. The characterization of amorphous materials is especially challenging because their lack of long-range order makes it…

In this paper, we use topological data analysis techniques to construct a suitable neural network classifier for the task of learning sensor signals of entire power plants according to their reference designation system. We use…

Persistent homology and persistent entropy have recently become useful tools for patter recognition. In this paper, we find requirements under which persistent entropy is stable to small perturbations in the input data and scale invariant.…

It has been a long-standing materials science challenge to establish structure-property relations in amorphous solids. Here we introduce a rotation-variant local structure representation that enables different predictions for different…

The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descriptors are vectorized using persistence images, which can…

Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…

A reaction route map (RRM) constructed using the GRRM program is a collection of elementary reaction pathways, each of which comprises two equilibrium (EQ) geometries and one transition state (TS) geometry connected by an intrinsic reaction…

We demonstrate a machine learning approach designed to extract hidden chemistry/physics to facilitate new materials discovery. In particular, we propose a novel method for learning latent knowledge from material structure data in which…

The analysis of nonlinear dynamics is an important issue in numerous fields of science. In this study, we propose a new method to analyze the time series data using persistent homology (PH). The key idea is the application of PH to the…

Feature matching in omnidirectional vision systems is a challenging problem, mainly because complicated optical systems make the theoretical modelling of invariance and construction of invariant feature descriptors hard or even impossible.…