Rank Detection Thresholds for Hankel or Toeplitz Data Matrices. v. der Veen , A. -., Romme, J., & Cui, Y. In *2020 28th European Signal Processing Conference (EUSIPCO)*, pages 1911-1915, Aug, 2020.

Paper doi abstract bibtex

Paper doi abstract bibtex

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.

@InProceedings{9287856, author = {A. -J. v. {der Veen} and J. Romme and Y. Cui}, booktitle = {2020 28th European Signal Processing Conference (EUSIPCO)}, title = {Rank Detection Thresholds for Hankel or Toeplitz Data Matrices}, year = {2020}, pages = {1911-1915}, 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.}, keywords = {Time series analysis;Europe;Signal processing;Harmonic analysis;Eigenvalues and eigenfunctions;Covariance matrices;Principal component analysis;PCA;structured Wishart matrix;rank detection;Generalized Extreme Value}, doi = {10.23919/Eusipco47968.2020.9287856}, issn = {2076-1465}, month = {Aug}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2020/pdfs/0001911.pdf}, }

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