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The fingerprint classification problem is to sort fingerprints into pre-determined groups, such as arch, loop, and whorl. It was asserted in the literature that minutiae points, which are commonly used for fingerprint matching, are not…

Transactional frequent subgraph mining identifies frequent subgraphs in a collection of graphs. This research problem has wide applicability and increasingly requires higher scalability over single machine solutions to address the needs of…

Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…

This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex…

Topological Data Analysis (TDA) has been successfully used for various tasks in signal/image processing, from visualization to supervised/unsupervised classification. Often, topological characteristics are obtained from persistent homology…

Density-based clustering has found numerous applications across various domains. The Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is capable of finding clusters of varied shapes that are not linearly…

Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations…

Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…

DBSCAN has been widely used in density-based clustering algorithms. However, with the increasing demand for Multi-density clustering, previous traditional DSBCAN can not have good clustering results on Multi-density datasets. In order to…

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…

This paper introduces advanced techniques of Topological Data Analysis (TDA) for unsupervised anomaly detection and customer segmentation in banking data. Using the Mapper algorithm and persistent homology, we develop unsupervised…

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…

Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…

Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm which has the high-performance rate for dataset where clusters have the constant density of data points. One of the significant attributes…

Persistent homology has been devised as a promising tool for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for…

This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…

Persistence diagrams (PDs) are used as signatures of point cloud data. Two clouds of points can be compared using the bottleneck distance d_B between their PDs. A potential drawback of this pipeline is that point clouds sampled from…

We introduce the monoidal Rips filtration, a filtered simplicial set for weighted directed graphs and other lattice-valued networks. Our construction generalizes the Vietoris-Rips filtration for metric spaces by replacing the maximum…

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…

Assessing the quality of 3D printed models before they are printed remains a challeng- ing problem, particularly when considering point cloud-based models. This paper introduces an approach to quality assessment, which uses techniques from…