Related papers: Time Series Featurization via Topological Data Ana…

Large time-varying graphs are increasingly common in financial, social and biological settings. Feature extraction that efficiently encodes the complex structure of sparse, multi-layered, dynamic graphs presents computational and…

With the latest advances in Deep Learning-based generative models, it has not taken long to take advantage of their remarkable performance in the area of time series. Deep neural networks used to work with time series heavily depend on the…

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…

We introduce a pipeline for time series classification that extracts features based on the iterated-sums signature (ISS) and then applies a linear classifier. These features are intrinsically nonlinear, capture chronological information,…

Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology,…

Machine learning algorithms are designed to capture complex relationships between features. In this context, the high dimensionality of data often results in poor model performance, with the risk of overfitting. Feature selection, the…

A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…

We extend the feature selection methodology to dependent data and propose a novel time series predictor selection scheme that accommodates statistical dependence in a more typical i.i.d sub-sampling based framework. Furthermore, the…

Persistent homology, a method from topological data analysis, extracts robust, multi-scale features from data. It produces stable representations of time series by applying varying thresholds to their values (a process known as a…

A critical aspect of power systems research is the availability of suitable data, access to which is limited by privacy concerns and the sensitive nature of energy infrastructure. This lack of data, in turn, hinders the development of…

Statistic modeling and data-driven learning are the two vital fields that attract many attentions. Statistic models intend to capture and interpret the relationships among variables, while data-based learning attempt to extract information…

This article proposes a new approach to modeling high-dimensional time series by treating a $p$-dimensional time series as a nonsingular linear transformation of certain common factors and idiosyncratic components. Unlike the approximate…

This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are…

In this paper, we present a novel feature extraction procedure to predict interval-valued time series by combing transfer learning and imaging approaches. Initially, we represent interval-valued time series using a bivariate point-valued…

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…

Real-world time series typically exhibit complex temporal variations, making the time series classification task notably challenging. Recent advancements have demonstrated the potential of multi-scale analysis approaches, which provide an…

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…

Anomaly detection in time series data is a critical challenge across various domains. Traditional methods typically focus on identifying anomalies in immediate subsequent steps, often underestimating the significance of temporal dynamics…

Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networks may be linked to specific tasks…

Time Series Anomaly Detection (TSAD) is essential for uncovering rare and potentially harmful events in unlabeled time series data. Existing methods are highly dependent on clean, high-quality inputs, making them susceptible to noise and…