Trendafilov, Nickolay T.
Due to copyright restrictions, this file is not available for public download
Click here to request a copy from the OU Author.
|DOI (Digital Object Identifier) Link:||http://dx.doi.org/10.1016/j.csda.2010.03.010|
|Google Scholar:||Look up in Google Scholar|
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
Mathematics, Computing and Technology
|Depositing User:||Sarah Frain|
|Date Deposited:||20 Jul 2010 11:52|
|Last Modified:||15 Jan 2016 13:02|
|Share this page:|