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Constrained energy variation for change point detection

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Abstract

The problem of change point detection can be solved either by online methods, based on a discrepancy measure, or by offline methods. The former tries to detect the change points one by one with a sliding window and leads to a lower computational time but are more sensitive to noise. Conversely, offline methods consider the entire data to detect all the change points which make them more robust against the noise but at a price of higher computational cost. In this paper, we propose an operational search method that combines the benefits of both approaches with the double aim to get higher noise resistance while keeping a blazingly fast time. The search method slides over the edges of the signal to determines their state by considering a global constrained energy. Thanks to the calculus of variation, the computation of this energy is reduced to the estimation of the effective jump for each edge. We study the performance and accuracy of our energy variation method to detect the change points in synthetic and real-world examples. The results compare favorably against state of the art algorithm in terms of speed and accuracy.

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Notes

  1. A clique \(\mathcal {C}\) is a complete graph where each node \(X_i\) is connected to all the other nodes \(X_j\). For our case, we only have unary cliques \(X_i\) and binary cliques \((X_i, X_{i+1})\).

  2. https://www.rdocumentation.org/packages/neuroblastoma.

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Authors and Affiliations

  1. School Digital Engineering and Artificial Intelligence-Euromed-Fès, Fès, Morocco

    A. Belcaid

  2. National School of Applied Sciences-Fès, Fès, Morocco

    H. Belkbir

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  1. A. Belcaid
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  2. H. Belkbir
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Belcaid, A., Belkbir, H. Constrained energy variation for change point detection. Multidim Syst Sign Process 33, 63–80 (2022). https://doi.org/10.1007/s11045-021-00785-w

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