The discrete Fourier transformation for seasonality and anomaly detection of an application to rare data

DOIhttps://doi.org/10.1108/DTA-12-2019-0243
Pages121-132
Publication Date21 May 2020
AuthorAryana Collins Jackson,Seán Lacey
SubjectLibrary & information science,Librarianship/library management,Library technology,Information behaviour & retrieval,Metadata,Information & knowledge management,Information & communications technology,Internet
The discrete Fourier
transformation for seasonality and
anomaly detection of an application
to rare data
Aryana Collins Jackson
Department of Computer Science,
Ecole Nationale dIng
enieurs de Brest, Brest,
France and
Department of Mathematics, Cork Institute of Technology, Cork, Ireland, and
Se
an Lacey
Department of Mathematics, Cork Institute of Technology, Cork, Ireland
Abstract
Purpose The discrete Fourier transformation (DFT) has been proven to be a successful method for
determining whether a discrete time series is seasonal and, if so, for detecting the period. This paper deals
exclusively with rare data, in which instances occur periodically at a low frequency.
Design/methodology/approach Data based on real-world situations is simulated for analysis.
Findings Cycle number detection is done with spectral analysis, period detection is completed using DFT
coefficients and signal shifts in the time domain are found using the convolution theorem. Additionally, a new
method for detecting anomalies in binary, rare data is presented: the sum of distances. Using this method,
expected events which have not occurred and unexpected events which have occurred at various sampling
frequencies can be detected. Anomalies which are not considered outliers to be found.
Research limitations/implications Aliasing can contribute to extra frequencies which point to extra
periods in the time domain. This can be reduced or removed with techniques such as windowing. In future
work, this will be explored.
Practical implications Applications include determining seasonality and thus investigating the
underlying causes of hard drive failure, power outages and other undesired events. This work will also lend
itself well to finding patterns among missing desired events, such as a scheduled hard drive backup or an
employees regular login to a server.
Originality/value This paper has shown how seasonality and anomalies are successfully detected in
seasonal, discrete, rare and binary data. Previously, the DFT has only been used for non-rare data.
Keywords Discrete Fourier transformation, Rare data, Discrete data, Seasonality detection, Anomaly
detection
Paper type Research paper
1. Introduction
The discrete Fourier transformation (DFT) has been proven (Gilgur and Perka, 2006;Strayer
et al., 2000;Xia, 2000) to be a successful method for determining whether a discrete time series,
also referred to here as the signal, contains seasonality and, if so, detecting its period. By
breaking down a time series into its sinusoidal components, seasonal attributes can be
obtained. Previously, the DFT has been applied to non-binary and non-rare data: signals in
which more than half of the sampled instances do not contain a zero and contain values
beyond 0 and 1.
This paper deals exclusively with discrete rare data: signals in which instances occur
periodicallyat a low frequency.A signalis considered low-frequencyif less than half of the total
DFT for
seasonality
and anomaly
detection
121
Funding:This research did not receive any specific grantfrom funding agencies in the public, commercial
or not-for-profit sectors.
This work was supported by Departmentof Mathematics, Cork Institute of Technology.
The current issue and full text archive of this journal is available on Emerald Insight at:
https://www.emerald.com/insight/2514-9288.htm
Received 20 December 2019
Revised 2 March 2020
Accepted 8 April 2020
Data Technologies and
Applications
Vol. 54 No. 2, 2020
pp. 121-132
© Emerald Publishing Limited
2514-9288
DOI 10.1108/DTA-12-2019-0243

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