TY - GEN

T1 - Random matrix theory and covariance matrix filtering for cancer gene expression

AU - Peterson, Leif E.

AU - Ford, Charles E.

PY - 2013

Y1 - 2013

N2 - We investigated random matrix theory (RMT) and covariance matrix filtering with shrinkage techniques to characterize eigendecomposition of a 190 ×190 covariance matrix based on 750 genes and 18 tumor classes. Principal component subtraction using the first PC resulted in the most favorable outcome concerning eigenvector participation ratios, class-specific influence scores, and unsupervised clustering of arrays. By fitting the Marčenko-Pastur density function, we determined that 86.8% of the covariance matrix eigenvalues were below the threshold value of λ + = 0.5025, suggesting that they reside in the noise region. Removal of noise eigenvector effects in the data were not as informative as removal of only the first eigenvector, however, there were interesting properties observed among the 25 non-zero eigenvalues after noise removal - mostly that they were lower than the first 25 eigenvalues of the remaining types of covariance matrices.

AB - We investigated random matrix theory (RMT) and covariance matrix filtering with shrinkage techniques to characterize eigendecomposition of a 190 ×190 covariance matrix based on 750 genes and 18 tumor classes. Principal component subtraction using the first PC resulted in the most favorable outcome concerning eigenvector participation ratios, class-specific influence scores, and unsupervised clustering of arrays. By fitting the Marčenko-Pastur density function, we determined that 86.8% of the covariance matrix eigenvalues were below the threshold value of λ + = 0.5025, suggesting that they reside in the noise region. Removal of noise eigenvector effects in the data were not as informative as removal of only the first eigenvector, however, there were interesting properties observed among the 25 non-zero eigenvalues after noise removal - mostly that they were lower than the first 25 eigenvalues of the remaining types of covariance matrices.

UR - http://www.scopus.com/inward/record.url?scp=84883348504&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-38342-7_15

DO - 10.1007/978-3-642-38342-7_15

M3 - Conference contribution

AN - SCOPUS:84883348504

SN - 9783642383410

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 173

EP - 184

BT - Computational Intelligence Methods for Bioinformatics and Biostatistics - 9th International Meeting, CIBB 2012, Revised Selected Papers

T2 - 9th International Meeting on Computational Intelligence Methods for Bioinformatics and Biostatistics, CIBB 2012

Y2 - 12 July 2012 through 14 July 2012

ER -