A Sequential Detection Theory for Statistically Periodic Random Processes

Banerjee, Taposh; Gurram, Prudhvi; Whipps, Gene

doi:10.1109/allerton.2019.8919699

Cited by 3 publications

(2 citation statements)

References 41 publications

(103 reference statements)

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“…The count of the number of Instagram messages posted near a CCTV camera in NYC has also been found to show approximately periodic behavior [8,9,[12][13][14][15] (see Fig. 1d).…”

Section: Social Network Datamentioning

confidence: 85%

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Quickest Joint Detection and Classification of Faults in Statistically Periodic Processes

Banerjee

Padhy

Taha

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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An algorithm is proposed to detect and classify a change in the distribution of a stochastic process that has periodic statistical behavior. The problem is posed in the framework of independent and periodically identically distributed (i.p.i.d.) processes, a recently introduced class of processes to model statistically periodic data. It is shown that the proposed algorithm is asymptotically optimal as the rate of false alarms and the probability of misclassification goes to zero. This problem has applications in anomaly detection in traffic data, social network data, ECG data, and neural data, where periodic statistical behavior has been observed. The effectiveness of the algorithm is demonstrated by application to real and simulated data.

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“…The count of the number of Instagram messages posted near a CCTV camera in NYC has also been found to show approximately periodic behavior [8,9,[12][13][14][15] (see Fig. 1d).…”

Section: Social Network Datamentioning

confidence: 85%

“…1: Real data from applications in medicine, neuroscience, and traffic exhibiting statistical periodicity. regular patterns of busy and quiet periods [8,9,[12][13][14][15]. A congestion or an accident can cause a drop or increase in these vehicle counts (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Quickest Joint Detection and Classification of Faults in Statistically Periodic Processes

Banerjee

Padhy

Taha

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Self Cite

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Quickest change detection in statistically periodic processes with unknown post-change distribution

Oleyaeimotlagh,

Banerjee,

Taha

et al. 2023

Sequential Analysis

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Abstract Cyclic Functional Relation and Taxonomies of Cyclic Signals Mathematical Models: Construction, Definitions and Properties

Lupenko

2024

Mathematics

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This work is devoted to the procedure of the construction of an abstract cyclic functional relation, which summarizes and extends the known results for a cyclically correlated random process and a cyclic (cyclically distributed) random process to the case of arbitrary cyclic functional relations. Two alternative definitions of the abstract cyclic functional relation are given, and the fundamental properties of its cyclic and phase structures are presented. The theorem on the invariance of cyclicity attributes of an abstract cyclic functional relation to shifts of its argument, and which are determined by the rhythm function of this functional relation, is formulated and proved. This theorem gives the sufficient and necessary conditions that the rhythm function of an abstract cyclic functional relation must satisfy. By specifying the range of values and attributes of the cyclicity of an abstract cyclic functional relation, the definitions of important classes of cyclic functional relations are formulated. A deductive approach to building a wide system of taxonomies of classes of deterministic, stochastic, fuzzy and interval cyclic functional relations as potential mathematical models of cyclic signals is demonstrated. A comparative analysis of an abstract cyclic functional relation with the known mathematical models of cyclic signals was carried out. The results obtained in the article significantly expand and systematize the mathematical tools of the description of cyclic signals and are the basis for the development of effective model-based technologies for processing and computer simulation of signals with a cyclic space-time structure.

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A Sequential Detection Theory for Statistically Periodic Random Processes

Cited by 3 publications

References 41 publications

Quickest Joint Detection and Classification of Faults in Statistically Periodic Processes

Quickest Joint Detection and Classification of Faults in Statistically Periodic Processes

Quickest change detection in statistically periodic processes with unknown post-change distribution

Abstract Cyclic Functional Relation and Taxonomies of Cyclic Signals Mathematical Models: Construction, Definitions and Properties

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