A Short Survey of Topological Data Analysis in Time Series and Systems Analysis
Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is relatively new. In some recent contributions, TDA has been utilized as an alternative to the conventional signal processing methods. Specifically, TDA is been considered to deal with noisy signals and time series. In these applications, TDA is used to find the shapes in data as the main properties, while the other properties are assumed much less informative. In this paper, we will review recent developments and contributions where topological data analysis especially persistent homology has been applied to time series analysis, dynamical systems and signal processing. We will cover problem statements such as stability determination, risk analysis, systems behaviour, and predicting critical transitions in financial markets.
Code (0)
등록된 구현이 없습니다.
Tasks
Time SeriesTime Series AnalysisTopological Data AnalysisSimilar Papers 제목 키워드 기반
Topological Data Analysis for Neural Network Analysis: A Comprehensive Survey
This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate stru…
ArticlesModel SelectionSurveyTopological Data AnalysisClustering Activity-Travel Behavior Time Series using Topological Data Analysis
Over the last few years, traffic data has been exploding and the transportation discipline has entered the era of big data. It brings out new opportunities for doing data-driven analysis, but it also challenges tradition…
ClusteringSurveyTime SeriesTime Series Analysis+1TOTOPO: Classifying univariate and multivariate time series with Topological Data Analysis
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-a…
BenchmarkingTime SeriesTime Series AnalysisTopological Data AnalysisProbing the topological properties of complex networks modeling short written texts
In recent years, graph theory has been widely employed to probe several language properties. More specifically, the so-called word adjacency model has been proven useful for tackling several practical problems, especiall…
Topological Deep Learning: A Review of an Emerging Paradigm
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustnes…
Deep LearningTopological Data Analysis