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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…

Algebraic Topology · Mathematics 2019-05-30 Paweł Dłotko , Wanling Qiu , Simon Rudkin

This article discusses a number of incorrect statements appearing in textbooks on data analysis, machine learning, or computational methods; the common theme in all these cases is the relevance and application of statistics to the study of…

Data Analysis, Statistics and Probability · Physics 2023-01-13 Alexandros Gezerlis , Martin Williams

Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the…

chao-dyn · Physics 2015-06-24 J. Timmer

Missing data are an unavoidable complication in many machine learning tasks. When data are `missing at random' there exist a range of tools and techniques to deal with the issue. However, as machine learning studies become more ambitious,…

This work investigates whether time series of natural phenomena can be understood as being generated by sequences of latent states which are ordered in systematic and regular ways. We focus on clinical time series and ask whether clinical…

Machine Learning · Computer Science 2025-08-29 Michael Hagmann , Michael Staniek , Stefan Riezler

Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of…

Machine Learning · Computer Science 2024-12-31 John Paparrizos , Fan Yang , Haojun Li

We present a de-trending algorithm for the removal of trends in time series. Trends in time series could be caused by various systematic and random noise sources such as cloud passages, changes of airmass, telescope vibration or CCD noise.…

Astrophysics · Physics 2009-09-29 Dae-Won Kim , Pavlos Protopapas , Charles Alcock , Yong-Ik Byun , Federica Bianco

High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based…

Quantitative Methods · Quantitative Biology 2010-01-06 Viet-Anh Nguyen , Zdena Koukolikova-Nicola , Franco Bagnoli , Pietro Lio

Time series prediction is a fundamental problem in scientific exploration and artificial intelligence (AI) technologies have substantially bolstered its efficiency and accuracy. A well-established paradigm in AI-driven time series…

Machine Learning · Computer Science 2024-05-14 Kexin Jiang , Chuhan Wu , Yaoran Chen

Recent advances in technology have brought major breakthroughs in data collection, enabling a large amount of data to be gathered over time and thus generating time series. Mining this data has become an important task for researchers and…

Machine Learning · Computer Science 2020-02-12 Ane Blázquez-García , Angel Conde , Usue Mori , Jose A. Lozano

In this course, I try to provide a few basics required for performing data analysis in asteroseismology. First, I address how one can properly treat times series: the sampling, the filtering effect, the use of Fourier transform, the…

Instrumentation and Methods for Astrophysics · Physics 2011-04-01 T. Appourchaux

Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…

Mesoscale and Nanoscale Physics · Physics 2021-03-19 Yuan Yang , Jie Ding

Text data is often seen as "take-away" materials with little noise and easy to process information. Main questions are how to get data and transform them into a good document format. But data can be sensitive to noise oftenly called…

Computation and Language · Computer Science 2023-06-22 Nicolas Turenne

Many time series classification tasks, where labels vary over time, are affected by label noise that also varies over time. Such noise can cause label quality to improve, worsen, or periodically change over time. We first propose and…

Machine Learning · Computer Science 2025-03-18 Sujay Nagaraj , Walter Gerych , Sana Tonekaboni , Anna Goldenberg , Berk Ustun , Thomas Hartvigsen

Time series is a collection of data instances that are ordered according to a time stamp. Stock prices, temperature, etc are examples of time series data in real life. Time series data are used for forecasting sales, predicting trends.…

Human-Computer Interaction · Computer Science 2024-04-25 Sathya Krishnan Suresh , Shunmugapriya P

While Internet of Things (IoT) devices and sensors create continuous streams of information, Big Data infrastructures are deemed to handle the influx of data in real-time. One type of such a continuous stream of information is time series…

Methodology · Statistics 2020-05-05 Elyas Sabeti , Peter X. K. Song , Alfred O. Hero

Changes in parameters of a physical device can eventually lead to catastrophic failure. This paper discusses a parameter estimation method based on synchronization between a model and time series data. In particular, we examine the…

chao-dyn · Physics 2007-05-23 Justin Goodwin , Reggie Brown , Lutz Junge

Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult…

Optimization and Control · Mathematics 2020-06-11 Dominik Kahl , Andreas Weber , Maik Kschischo

We study the problem of coincidence detection in time series data, where we aim to determine whether the appearance of simultaneous or near-simultaneous events in two time series is indicative of some shared underlying signal or…

Statistics Theory · Mathematics 2026-01-21 Ruiting Liang , Samuel Dyson , Rina Foygel Barber , Daniel E. Holz

Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In…

Machine Learning · Computer Science 2020-08-19 Steven Cheng-Xian Li , Benjamin M. Marlin