Related papers: Topological Data Analysis (TDA) for Time Series

Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…

We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural…

Time series data is a collection of chronological observations which is generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting, and clustering have been…

We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information…

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…

Chatter identification and detection in machining processes has been an active area of research in the past two decades. Part of the challenge in studying chatter is that machining equations that describe its occurrence are often nonlinear…

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…

Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…

Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…

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,…

We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…

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…

Given a data set with a notion of distance, such as a point cloud in Euclidean space, topological data analysis (TDA) uses techniques from algebraic topology and metric geometry to infer the topology of a hypothetical manifold from which…

In this paper we evaluate the performance of topological features for generalizable and robust classification of firn image data, with the broader goal of understanding the advantages, pitfalls, and trade-offs in topological featurization.…

We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…

Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…

Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…

Over the last few years, with the growth of time-series collecting and storing, there has been a great demand for tools and software for temporal data engineering and modeling. This paper presents a generic workflow for time series data…

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…

In this paper, we propose a method that extends the persistence-based topological data analysis (TDA) that is typically used for characterizing shapes to general networks. We introduce the concept of the community tree, a tree structure…