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Online wavelet-based density estimation for non-stationary streaming data

Author

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  • García-Treviño, E.S.
  • Barria, J.A.

Abstract

There has been an important emergence of applications in which data arrives in an online time-varying fashion (e.g. computer network traffic, sensor data, web searches, ATM transactions) and it is not feasible to exchange or to store all the arriving data in traditional database systems to operate on it. For this kind of applications, as it is for traditional static database schemes, density estimation is a fundamental block for data analysis. A novel online approach for probability density estimation based on wavelet bases suitable for applications involving rapidly changing streaming data is presented. The proposed approach is based on a recursive formulation of the wavelet-based orthogonal estimator using a sliding window and includes an optimised procedure for reevaluating only relevant scaling and wavelet functions each time new data items arrive. The algorithm is tested and compared using both simulated and real world data.

Suggested Citation

  • García-Treviño, E.S. & Barria, J.A., 2012. "Online wavelet-based density estimation for non-stationary streaming data," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 327-344.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:327-344
    DOI: 10.1016/j.csda.2011.08.009
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    References listed on IDEAS

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    1. Caudle, Kyle A. & Wegman, Edward, 2009. "Nonparametric density estimation of streaming data using orthogonal series," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3980-3986, October.
    2. Masry, Elias, 1994. "Probability density estimation from dependent observations using wavelets orthonormal bases," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 181-194, October.
    3. Pinheiro, Aluisio & Vidakovic, Brani, 1997. "Estimating the square root of a density via compactly supported wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 25(4), pages 399-415, September.
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    1. García Treviño, E.S. & Alarcón Aquino, V. & Barria, J.A., 2019. "The radial wavelet frame density estimator," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 111-139.
    2. Cardot, Hervé & Cénac, Peggy & Monnez, Jean-Marie, 2012. "A fast and recursive algorithm for clustering large datasets with k-medians," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1434-1449.

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