Rank detection thresholds for Hankel or Toeplitz data matrices

A.J. van der Veen, J.P.A. Romme, Ye Cui

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Abstract

In Principal Component Analysis (PCA), the dimension of the signal subspace is detected by counting the number of eigenvalues of a covariance matrix that are above a threshold. Random matrix theory provides accurate estimates for this threshold if the underlying data matrix has independent identically distributed columns. However, in time series analysis, the underlying data matrix has a Hankel or Toeplitz structure, and the columns are not independent. Using an empirical approach, we observe that the largest eigenvalue is fitted well by a Generalized Extreme Value (GEV) distribution, and we obtain accurate estimates for the thresholds to be used in a sequential rank detection test. In contrast to AIC or MDL, this provides a parameter that controls the probability of false alarm. Also a lower bound is presented for the rank detection rate of threshold-based detection for rank-1 problems.
Original languageEnglish
Title of host publication28th European Signal Processing Conference (EUSIPCO 2020)
Place of PublicationAmsterdam (Netherlands)
PublisherEurasip
Pages1911-1915
Number of pages5
ISBN (Electronic)978-9-0827-9705-3
Publication statusPublished - 1 Aug 2020
EventEUSIPCO 2020: The 28th European Signal Processing Conference - Amsterdam, Netherlands
Duration: 18 Jan 202122 Jan 2021
Conference number: 28th

Conference

ConferenceEUSIPCO 2020
CountryNetherlands
CityAmsterdam
Period18/01/2122/01/21
OtherDate change due to COVID-19 (former date August 24-28 2020)

Keywords

  • PCA
  • structured Wishart matrix
  • rank detection
  • Generalized Extreme Value

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  • Cite this

    van der Veen, A. J., Romme, J. P. A., & Cui, Y. (2020). Rank detection thresholds for Hankel or Toeplitz data matrices. In 28th European Signal Processing Conference (EUSIPCO 2020) (pp. 1911-1915). Eurasip.