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.
![Rank Detection Thresholds for Hankel or Toeplitz Data Matrices [pdf]](https://bibbase.org/img/filetypes/pdf.svg "pdf")
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},
}Downloads: 0
{"_id":"G7kRis4y6MRq6zghb","bibbaseid":"vderveen-romme-cui-rankdetectionthresholdsforhankelortoeplitzdatamatrices-2020","authorIDs":[],"author_short":["v. der Veen , A. -.","Romme, J.","Cui, Y."],"bibdata":{"bibtype":"inproceedings","type":"inproceedings","author":[{"firstnames":["A.","-J."],"propositions":["v.","der Veen"],"lastnames":[],"suffixes":[]},{"firstnames":["J."],"propositions":[],"lastnames":["Romme"],"suffixes":[]},{"firstnames":["Y."],"propositions":[],"lastnames":["Cui"],"suffixes":[]}],"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","bibtex":"@InProceedings{9287856,\n author = {A. -J. v. {der Veen} and J. Romme and Y. Cui},\n booktitle = {2020 28th European Signal Processing Conference (EUSIPCO)},\n title = {Rank Detection Thresholds for Hankel or Toeplitz Data Matrices},\n year = {2020},\n pages = {1911-1915},\n 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.},\n 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},\n doi = {10.23919/Eusipco47968.2020.9287856},\n issn = {2076-1465},\n month = {Aug},\n url = {https://www.eurasip.org/proceedings/eusipco/eusipco2020/pdfs/0001911.pdf},\n}\n\n","author_short":["v. der Veen , A. -.","Romme, J.","Cui, Y."],"key":"9287856","id":"9287856","bibbaseid":"vderveen-romme-cui-rankdetectionthresholdsforhankelortoeplitzdatamatrices-2020","role":"author","urls":{"Paper":"https://www.eurasip.org/proceedings/eusipco/eusipco2020/pdfs/0001911.pdf"},"keyword":["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"],"metadata":{"authorlinks":{}},"downloads":0},"bibtype":"inproceedings","biburl":"https://raw.githubusercontent.com/Roznn/EUSIPCO/main/eusipco2020url.bib","creationDate":"2021-02-13T19:41:51.497Z","downloads":0,"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"],"search_terms":["rank","detection","thresholds","hankel","toeplitz","data","matrices","v. der veen ","romme","cui"],"title":"Rank Detection Thresholds for Hankel or Toeplitz Data Matrices","year":2020,"dataSources":["wXzutN6o5hxayPKdC","NBHz6C7PWuqwYyaqa"]}