Related papers: A Subsequence Approach to Topological Data Analysi…
Supervised learning with irregularly sampled time series have been a challenge to Machine Learning methods due to the obstacle of dealing with irregular time intervals. Some papers introduced recently recurrent neural network models that…
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…
Despite the notable advancements in numerous Transformer-based models, the task of long multi-horizon time series forecasting remains a persistent challenge, especially towards explainability. Focusing on commonly used saliency maps in…
Software libraries for Topological Data Analysis (TDA) offer limited support for interactive visualization. Most libraries only allow to visualize topological descriptors (e.g., persistence diagrams), and lose the connection with the…
Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly…
In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two…
Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…
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…
Time series analysis has gained significant attention due to its critical applications in diverse fields such as healthcare, finance, and sensor networks. The complexity and non-stationarity of time series make it challenging to capture the…
With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…
The time delay (or Sliding Window) embedding is a technique from dynamical systems to reconstruct attractors from time series data. Recently, descriptors from Topological Data Analysis (TDA) -- specifically, persistence diagrams -- have…
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…
Investigating the network stability or synchronization dynamics of multi-agent systems with time delays is of significant importance in numerous real-world applications. Such investigations often rely on solving the transcendental…
Topological Data Analysis (TDA) has been praised by researchers for its ability to capture intricate shapes and structures within data. TDA is considered robust in handling noisy and high-dimensional datasets, and its interpretability is…
The continued digitization of societal processes translates into a proliferation of time series data that cover applications such as fraud detection, intrusion detection, and energy management, where anomaly detection is often essential to…
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…
Dynamic community detection methods often lack effective mechanisms to ensure temporal consistency, hindering the analysis of network evolution. In this paper, we propose a novel deep graph clustering framework with temporal consistency…
The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their…
Time series anomaly detection is a challenging problem due to the complex temporal dependencies and the limited label data. Although some algorithms including both traditional and deep models have been proposed, most of them mainly focus on…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…