Related papers: Fuzzy c-Means Clustering for Persistence Diagrams

Efficiently processing structured point cloud data while preserving multiscale information is a key challenge across domains, from graphics to atomistic modeling. Using a curated dataset of simulated galaxy positions and properties,…

Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…

Computer vision applications are omnipresent nowadays. The current paper explores the use of fuzzy logic in computer vision, stressing its role in handling uncertainty, noise, and imprecision in image data. Fuzzy logic is able to model…

The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…

A current assumption of most clustering methods is that the training data and future data are taken from the same distribution. However, this assumption may not hold in most real-world scenarios. In this paper, we propose an information…

Recent progress towards universal machine-learned interatomic potentials holds considerable promise for materials discovery. Yet the accuracy of these potentials for predicting phase stability may still be limited. In contrast, cluster…

In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…

Image thresholding has played an important role in image segmentation. This paper presents a hybrid approach for image segmentation based on the thresholding by fuzzy c-means (THFCM) algorithm for image segmentation. The goal of the…

Fuzzy systems (FSs) have enjoyed wide applications in various fields, including pattern recognition, intelligent control, data mining and bioinformatics, which is attributed to the strong interpretation and learning ability. In traditional…

The growing complexity of machine learning (ML) models in big data analytics, especially in domains such as environmental monitoring, highlights the critical need for interpretability and explainability to promote trust, ethical…

With the increasing importance of data privacy protection, various privacy-preserving machine learning methods have been proposed. In the clustering domain, various algorithms with a federated learning framework (i.e., federated clustering)…

Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The…

Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological summary that can be easily combined with tools from statistics and machine learning.…

Fuzzy systems have good modeling capabilities in several data science scenarios, and can provide human-explainable intelligence models with explainability and interpretability. In contrast to transaction data, which have been extensively…

Based on signaling process on complex networks, a method for identification community structure is proposed. For a network with $n$ nodes, every node is assumed to be a system which can send, receive, and record signals. Each node is taken…

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of…

Recently, contiguous sequential pattern mining (CSPM) gained interest as a research topic, due to its varied potential real-world applications, such as web log and biological sequence analysis. To date, studies on the CSPM problem remain in…

Diffusion models are a powerful framework for tackling ill-posed problems, with recent advancements extending their use to point cloud upsampling. Despite their potential, existing diffusion models struggle with inefficiencies as they map…

Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…

Modern online mass spectrometry generates multi-terabyte data streams critical for understanding Earth's environmental systems. However, extracting actionable chemical insights from these repositories is impeded by a computational…