Detecting series periodicity with horizontal visibility graphs

The horizontal visibility algorithm has been recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the powerful tools of graph theory. Recent works have shown that the visibility graphs inherit several degrees of correlations from their associated series, and therefore such graph theoretical characterization is in principle possible. However, both the mathematical grounding of this promising theory and its applications are on its infancy. Following this line, here we address the question of detecting hidden periodicity in series polluted with a certain amount of noise. We first put forward some generic properties of horizontal visibility graphs which allow us to define a (graph theoretical) noise reduction filter. Accordingly, we evaluate its performance for the task of calculating the period of noisy periodic signals, and compare our results with standard time domain (autocorrelation) methods. Finally, potentials, limitations and applications are discussed.Comment: To be published in International Journal of Bifurcation and Chao

Periodic Pattern Mining a Algorithms and Applications

Owing to a large number of applications periodic pattern mining has been extensively studied for over a decade Periodic pattern is a pattern that repeats itself with a specific period in a give sequence Periodic patterns can be mined from datasets like biological sequences continuous and discrete time series data spatiotemporal data and social networks Periodic patterns are classified based on different criteria Periodic patterns are categorized as frequent periodic patterns and statistically significant patterns based on the frequency of occurrence Frequent periodic patterns are in turn classified as perfect and imperfect periodic patterns full and partial periodic patterns synchronous and asynchronous periodic patterns dense periodic patterns approximate periodic patterns This paper presents a survey of the state of art research on periodic pattern mining algorithms and their application areas A discussion of merits and demerits of these algorithms was given The paper also presents a brief overview of algorithms that can be applied for specific types of datasets like spatiotemporal data and social network

Robust discovery of periodically expressed genes using the laplace periodogram

<p>Abstract</p> <p>Background</p> <p>Time-course gene expression analysis has become important in recent developments due to the increasingly available experimental data. The detection of genes that are periodically expressed is an important step which allows us to study the regulatory mechanisms associated with the cell cycle.</p> <p>Results</p> <p>In this work, we present the Laplace periodogram which employs the least absolute deviation criterion to provide a more robust detection of periodic gene expression in the presence of outliers. The Laplace periodogram is shown to perform comparably to existing methods for the <it>Sacharomyces cerevisiae</it> and <it>Arabidopsis</it> time-course datasets, and to outperform existing methods when outliers are present.</p> <p>Conclusion</p> <p>Time-course gene expression data are often noisy due to the limitations of current technology, and may include outliers. These artifacts corrupt the available data and make the detection of periodicity difficult in many cases. The Laplace periodogram is shown to perform well for both data with and without the presence of outliers, and also for data that are non-uniformly sampled.</p

An Efficient Probabilistic Algorithm to Detect Periodic Patterns in Spatio-Temporal Datasets

Author Contributions: Conceptualization, C.G.-S.; methodology, C.G.-S.; software, C.G.-S.; validation, C.G.-S., P.G. and M.A.P.; formal analysis, C.G.-S.; investigation, C.G.-S., P.G. and M.A.P.; data curation, C.G.-S.; writing—original draft preparation, C.G.-S., P.G. and M.A.P.; writing—review and editing, M.A.P.; funding acquisition, C.G.-S. and M.A.P. All authors have read and agreed to the published version of the manuscript.Peer reviewe