Topological Data Analysis for High-Dimensional Dynamic Process Monitoring

• URL: http://arxiv.org/abs/2606.20443v1
• Date: Thu, 18 Jun 2026 16:22:57 GMT
• Title: Topological Data Analysis for High-Dimensional Dynamic Process Monitoring
• Abstract summary: We present a new approach for process monitoring that combines tools of topological data analysis and machine learning.<n>We show that this trajectory-based event detection approach is effective at detecting diverse types of events.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data. In this work, we present a new approach for process monitoring that combines tools of topological data analysis (TDA) and machine learning. In the proposed approach, we represent multivariate time-series data as manifolds and use topological descriptors to summarize the structure of such data; we then use a neural ordinary differential equation to learn the dynamic evolution of the topological structure of the system. Using real data from an industrial process, we show that this trajectory-based event detection approach is effective at detecting diverse types of events. We contrast this approach against reconstruction-based approaches such as principal component analysis and autoencoders and against a trajectory-based approach that uses Koopman autoencoders.

Related papers

• Sequential Inference for Gaussian Processes: A Signal Processing Perspective [45.00250014235801]
  Gaussian processes (GPs) are a flexible yet principled framework for modeling random functions.<n>We provide a self-contained, tutorial-style overview of GPs, with a particular focus on recent methodological advances in sequential, incremental, or streaming inference.<n>Many of the developments we survey have direct applications to state-space modeling, sequential regression and forecasting, anomaly detection in time series, sequential Bayesian optimization, adaptive and active sensing, and sequential detection and decision-making.
  arXiv  Detail & Related papers  (2026-04-30T17:48:09Z)
• Tracing the Roots: A Multi-Agent Framework for Uncovering Data Lineage in Post-Training LLMs [81.43302841109349]
  Post-training data plays a pivotal role in shaping the capabilities of Large Language Models (LLMs)<n>We propose an automated multi-agent framework to reconstruct the evolutionary graph of dataset development.
  arXiv  Detail & Related papers  (2026-04-12T06:24:07Z)
• Graph Neural Network and Transformer Integration for Unsupervised System Anomaly Discovery [14.982273490507986]
  This study proposes an unsupervised anomaly detection method for distributed backend service systems.<n>It addresses practical challenges such as complex structural dependencies, diverse behavioral evolution, and the absence of labeled data.<n>Results show that the proposed method outperforms existing models on several key metrics.
  arXiv  Detail & Related papers  (2025-08-13T00:35:58Z)
• Navigating the Latent Space Dynamics of Neural Models [45.503229142378814]
  We present an alternative interpretation of neural models as dynamical systems acting on the latent manifold.<n>We show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map.<n>We propose to leverage the vector field as a representation for the network, providing a novel tool to analyze the properties of the model and the data.
  arXiv  Detail & Related papers  (2025-05-28T18:57:41Z)
• Transforming Multidimensional Time Series into Interpretable Event Sequences for Advanced Data Mining [5.2863523790908955]
  This paper introduces a novel proposed representation model designed to address the limitations of traditional methods in multidimensional time series (MTS) analysis. The proposed framework has significant potential for applications across various fields, including services for monitoring and optimizing IT infrastructure, medical diagnosis through continuous patient monitoring, trend analysis, and internet businesses for tracking user behavior and forecasting.
  arXiv  Detail & Related papers  (2024-09-22T06:27:07Z)
• Loop Polarity Analysis to Avoid Underspecification in Deep Learning [0.0]
  In this paper, we turn to loop polarity analysis as a tool for specifying the causal structure of a data-generating process. We show how measuring the polarity of the different feedback loops that compose a system can lead to more robust inferences on the part of neural networks.
  arXiv  Detail & Related papers  (2023-09-18T23:49:42Z)
• Score-based Data Assimilation [7.215767098253208]
  We introduce score-based data assimilation for trajectory inference. We learn a score-based generative model of state trajectories based on the key insight that the score of an arbitrarily long trajectory can be decomposed into a series of scores over short segments.
  arXiv  Detail & Related papers  (2023-06-18T14:22:03Z)
• Detection and Evaluation of Clusters within Sequential Data [58.720142291102135]
  Clustering algorithms for Block Markov Chains possess theoretical optimality guarantees. In particular, our sequential data is derived from human DNA, written text, animal movement data and financial markets. It is found that the Block Markov Chain model assumption can indeed produce meaningful insights in exploratory data analyses.
  arXiv  Detail & Related papers  (2022-10-04T15:22:39Z)
• Automated Evolutionary Approach for the Design of Composite Machine Learning Pipelines [48.7576911714538]
  The proposed approach is aimed to automate the design of composite machine learning pipelines. It designs the pipelines with a customizable graph-based structure, analyzes the obtained results, and reproduces them. The software implementation on this approach is presented as an open-source framework.
  arXiv  Detail & Related papers  (2021-06-26T23:19:06Z)
• On Contrastive Representations of Stochastic Processes [53.21653429290478]
  Learning representations of processes is an emerging problem in machine learning. We show that our methods are effective for learning representations of periodic functions, 3D objects and dynamical processes.
  arXiv  Detail & Related papers  (2021-06-18T11:00:24Z)
• Scalable nonparametric Bayesian learning for heterogeneous and dynamic velocity fields [8.744017403796406]
  We develop a model for learning heterogeneous and dynamic patterns of velocity field data. We show the effectiveness of our techniques to the NGSIM dataset of complex multi-vehicle interactions.
  arXiv  Detail & Related papers  (2021-02-15T17:45:46Z)
• Deep Cellular Recurrent Network for Efficient Analysis of Time-Series Data with Spatial Information [52.635997570873194]
  This work proposes a novel deep cellular recurrent neural network (DCRNN) architecture to process complex multi-dimensional time series data with spatial information. The proposed architecture achieves state-of-the-art performance while utilizing substantially less trainable parameters when compared to comparable methods in the literature.
  arXiv  Detail & Related papers  (2021-01-12T20:08:18Z)
• Forecasting Sequential Data using Consistent Koopman Autoencoders [52.209416711500005]
  A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. We propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators.
  arXiv  Detail & Related papers  (2020-03-04T18:24:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.