Related papers: Exact multi-parameter persistent homology of time-…
Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…
Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…
The machinery of topological data analysis becomes increasingly popular in a broad range of machine learning tasks, ranging from anomaly detection and manifold learning to graph classification. Persistent homology is one of the key…
Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…
TDA (topological data analysis) is a relatively new area of research related to importing classical ideas from topology into the realm of data analysis. Under the umbrella term TDA, there falls, in particular, the notion of persistent…
We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pronounced topological…
Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…
We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the…
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…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
Bearing fault detection is a critical task in predictive maintenance, where accurate and timely fault identification can prevent costly downtime and equipment damage. Traditional attention mechanisms in Transformer neural networks often…
Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a…
This work is devoted to a comprehensive analysis of topological data analysis fortime series classification. Previous works have significant shortcomings, such aslack of large-scale benchmarking or missing state-of-the-art methods. In this…
We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called persistence complex is used to reveal…
Flow in porous media is difficult to address using standard analytical or numerical methods due to its complexity. However, since synthetic representations of porous media are easy to produce and data from physical experiments are becoming…
The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…
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…
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…
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…