Estimating common principal components in high dimensions

• Absil P-A, Mahony R, Sepulchre R (2008) Optimization algorithms on matrix manifolds. Princeton University Press, Princeton

• Andrews JL, McNicholas PD (2012) Model-based clustering, classification, and discriminant analysis via mixtures of multivariate t-distributions. Stat Comput 22(5):1021–1029

  Article  MATH  MathSciNet  Google Scholar 

• Arnold S, Phillips P (1999) Hierarchical comparison of genetic variance-covariance matrices. II. Coastal-inland divergence in the garter snake, Thamnophis elegans. Evolution 53:1516–1527

  Article  Google Scholar 

• Banfield JD, Raftery AE (1993) Model-based Gaussian and non-Gaussian clustering. Biometrics 49(3): 803–821

  Google Scholar 

• Biernacki C, Celeux G, Govaert G, Langrognet F (2006) Model-based cluster analysis and discriminant analysis with the MIXMOD software. Comput Stat Data Anal 51:587–600

  Article  MATH  MathSciNet  Google Scholar 

• Boik RJ (2003) Principal component models for correlation matrices. Biometrika 90:679–701

  Article  MathSciNet  Google Scholar 

• Boik RJ (2007) Spectral models for covariance matrices. Biometrika 89:159–182

  Article  MathSciNet  Google Scholar 

• Bouveyron C, Girard S, Schmid C (2007) High-dimensional data clustering. Comput Stat and Data Anal 52:502–519

  Article  MATH  MathSciNet  Google Scholar 

• Browne RP, McNicholas PD (2012) Orthogonal Stiefel manifold optimization for eigen-decomposed covariance parameter estimation in mixture models. Statistics and Computing. To appear. doi:10.1007/s11222-012-9364-2

• Browne RP, McNicholas PD (2013) mixture: Mixture models for clustering and classification. R package version 1.0

• Celeux G, Govaert G (1995) Gaussian parsimonious clustering models. Pattern Recogn 28(5):781–793

  Article  Google Scholar 

• Dasgupta A, Raftery AE (1998) Detecting features in spatial point processes with clutter via model-based clustering. J Am Stat Assoc 93:294–302

  Article  MATH  Google Scholar 

• Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Royal Stat Soc Series B 39(1):1–38

  MATH  MathSciNet  Google Scholar 

• Flury BW, Gautschi W (1984) Common principal components in k groups. J Am Stat Assoc 79(388): 892–898

  Google Scholar 

• Flury BW, Gautschi W (1986) An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form. J Sci Stat Comput 7(1):169–184

  Article  MATH  MathSciNet  Google Scholar 

• Hunter D (2004) MM algorithms for generalized Bradley-Terry models. Ann Stat 32:386–408

  Google Scholar 

• Hunter D, Lange K (2000) Quantile regression via an MM algorithm. J Comput Graph Stat 9:60–77

  MathSciNet  Google Scholar 

• Kiers H (2002) Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems. Comput Stat Data Anal 41:157–170

  Article  MATH  MathSciNet  Google Scholar 

• Klingenberg C, Neuenschwander B, Flury B (1996) Ontogeny and individual variation: Analysis of patterned covariance matrices with common principal components. Syste Biol 45:135–150

  Article  Google Scholar 

• Krzanowski WJ (1990) Between-group analysis with heterogeneous covariance. matrices: The common principal component model. J Classif 7:81–98

  Article  MATH  MathSciNet  Google Scholar 

• Kulkarni B, Rao G (2000) The common principal components approach for clustering under multiple sampling. J Indian Soc Agric Stat 53:1–11

  Google Scholar 

• Lebret R, Iovleff S, Langrognet F (2012) Rmixmod: MIXture MODelling Package. R package version 1.1.1

• Lefkomtch LP (2004) Consensus principal components. Biometrical J 35:567–580

  Article  Google Scholar 

• Merbouha A, Mkhadri A (2004) Regularization of the location model in discrimination with mixed discrete and continuous variables. Comput Stat Data Anal 45:463–576

  MathSciNet  Google Scholar 

• Oksanen J, Huttunen P (1989) Finding a common ordination for several data sets by individual differences scaling. Plant Ecol 83:137–145

  Article  Google Scholar 

• R Development Core Team (2012) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna

• Schott J (1998) Estimating correlation matrices that have common eigenvectors. Comput Stat Data Anal 27:445–459

  Article  MATH  MathSciNet  Google Scholar 

• Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464

  Article  MATH  Google Scholar 

• Sengupta S, Boyle J (1998) Using common principal components for comparing GCM simulations. J Climate 11:816–830

  Google Scholar 

• von Mises R, Pollaczek-Geiringer H (1929) Praktische verfahren der gleichungsauflösung. Zeitschrift für Angewandte Mathematik und Mechanik 9(1):58–77

  Article  MATH  Google Scholar 

• Yang K, Shahabi C (2006) An efficient k nearest neighbor search for multivariate time series. Info Comput 205:65–98

  Article  MathSciNet  Google Scholar 

Download references