Physiological time-series analysis using approximate entropy and sample entropy. Richman J S,Moorman J R American journal of physiology. Heart and circulatory physiology Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series. 10.1152/ajpheart.2000.278.6.H2039

A Systematic Review of Time Series Classification Techniques Used in Biomedical Applications. Sensors (Basel, Switzerland) Digital clinical measures collected via various digital sensing technologies such as smartphones, smartwatches, wearables, and ingestible and implantable sensors are increasingly used by individuals and clinicians to capture the health outcomes or behavioral and physiological characteristics of individuals. Time series classification (TSC) is very commonly used for modeling digital clinical measures. While deep learning models for TSC are very common and powerful, there exist some fundamental challenges. This review presents the non-deep learning models that are commonly used for time series classification in biomedical applications that can achieve high performance. We performed a systematic review to characterize the techniques that are used in time series classification of digital clinical measures throughout all the stages of data processing and model building. We conducted a literature search on PubMed, as well as the Institute of Electrical and Electronics Engineers (IEEE), Web of Science, and SCOPUS databases using a range of search terms to retrieve peer-reviewed articles that report on the academic research about digital clinical measures from a five-year period between June 2016 and June 2021. We identified and categorized the research studies based on the types of classification algorithms and sensor input types. We found 452 papers in total from four different databases: PubMed, IEEE, Web of Science Database, and SCOPUS. After removing duplicates and irrelevant papers, 135 articles remained for detailed review and data extraction. Among these, engineered features using time series methods that were subsequently fed into widely used machine learning classifiers were the most commonly used technique, and also most frequently achieved the best performance metrics (77 out of 135 articles). Statistical modeling (24 out of 135 articles) algorithms were the second most common and also the second-best classification technique. In this review paper, summaries of the time series classification models and interpretation methods for biomedical applications are summarized and categorized. While high time series classification performance has been achieved in digital clinical, physiological, or biomedical measures, no standard benchmark datasets, modeling methods, or reporting methodology exist. There is no single widely used method for time series model development or feature interpretation, however many different methods have proven successful. 10.3390/s22208016

Identifying local associations in biological time series: algorithms, statistical significance, and applications. Briefings in bioinformatics Local associations refer to spatial-temporal correlations that emerge from the biological realm, such as time-dependent gene co-expression or seasonal interactions between microbes. One can reveal the intricate dynamics and inherent interactions of biological systems by examining the biological time series data for these associations. To accomplish this goal, local similarity analysis algorithms and statistical methods that facilitate the local alignment of time series and assess the significance of the resulting alignments have been developed. Although these algorithms were initially devised for gene expression analysis from microarrays, they have been adapted and accelerated for multi-omics next generation sequencing datasets, achieving high scientific impact. In this review, we present an overview of the historical developments and recent advances for local similarity analysis algorithms, their statistical properties, and real applications in analyzing biological time series data. The benchmark data and analysis scripts used in this review are freely available at http://github.com/labxscut/lsareview. 10.1093/bib/bbad390