Trendafilov, Nickolay T.
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|DOI (Digital Object Identifier) Link:||http://dx.doi.org/doi:10.1016/j.csda.2010.03.010|
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The standard common principal components (CPCs) may not always be useful for simultaneous dimensionality reduction in k groups. Moreover, the original FG algorithm finds the CPCs in arbitrary order, which does not reflect their importance with respect to the explained variance. A possible alternative is to find an approximate common subspace for all k groups. A new stepwise estimation procedure for obtaining CPCs is proposed, which imitates standard PCA. The stepwise CPCs facilitate simultaneous dimensionality reduction, as their variances are decreasing at least approximately in all k groups. Thus, they can be a better alternative for dimensionality reduction than the standard CPCs. The stepwise CPCs are found sequentially by a very simple algorithm, based on the well-known power method for a single covariance/correlation matrix. Numerical illustrations on well-known data are considered.
|Item Type:||Journal Article|
|Copyright Holders:||2010 Elsevier B.V.|
|Keywords:||simultaneous diagonalization; dimensionality reduction; power iterations for k symmetric positive definite matrices|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics|
|Depositing User:||Sarah Frain|
|Date Deposited:||20 Jul 2010 11:52|
|Last Modified:||17 May 2013 03:46|
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