Related papers: Time Series Featurization via Topological Data Ana…

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to…

This work is dedicated to the topological analysis of complex transitional networks for dynamic state detection. Transitional networks are formed from time series data and they leverage graph theory tools to reveal information about the…

Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…

Time series data account for a major part of data supply available today. Time series mining handles several tasks such as classification, clustering, query-by-content, prediction, and others. Performing data mining tasks on raw time series…

This paper formulates the problem of learning discriminative features (\textit{i.e.,} segments) from networked time series data considering the linked information among time series. For example, social network users are considered to be…

Extracting informative features from images has been of capital importance in computer vision. In this paper, we propose a way to extract such features from images by a method based on algebraic topology. To that end, we construct a…

Time series data usually contains local and global patterns. Most of the existing feature networks pay more attention to local features rather than the relationships among them. The latter is, however, also important yet more difficult to…

We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence…

Persistent homology, a powerful mathematical tool for data analysis, summarizes the shape of data through tracking topological features across changes in different scales. Classical algorithms for persistent homology are often constrained…

How to handle time features shall be the core question of any time series forecasting model. Ironically, it is often ignored or misunderstood by deep-learning based models, even those baselines which are state-of-the-art. This behavior…

In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time…

The feature extraction methods of radiomics are mainly based on static tomographic images at a certain moment, while the occurrence and development of disease is a dynamic process that cannot be fully reflected by only static…

In this paper, we propose a novel framework for dynamical analysis of human actions from 3D motion capture data using topological data analysis. We model human actions using the topological features of the attractor of the dynamical system.…

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…

It has been demonstrated that the amount of data is crucial in data-driven machine learning methods. Data is always valuable, but in some tasks, it is almost like gold. This occurs in engineering areas where data is scarce or very expensive…

Temporal networks representing a stream of timestamped edges are seemingly ubiquitous in the real-world. However, the massive size and continuous nature of these networks make them fundamentally challenging to analyze and leverage for…

In this paper, we introduce a novel unsupervised, graph-based filter feature selection technique which exploits the power of topologically constrained network representations. We model dependency structures among features using a family of…

Time series data, defined by equally spaced points over time, is essential in fields like medicine, telecommunications, and energy. Analyzing it involves tasks such as classification, clustering, prototyping, and regression. Classification…

Time series (TS) data have consistently been in short supply, yet their demand remains high for training systems in prediction, modeling, classification, and various other applications. Synthesis can serve to expand the sample population,…

This paper proposes a novel approach for detecting the topology of distribution networks based on the analysis of time series measurements. The time-based analysis approach draws on data from high-precision phasor measurement units (PMUs or…