Common principal components & related multivariate models
Common principal components & related multivariate models
Matrix computations (3rd ed.)
Journal of Multivariate Analysis
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Projected gradient approach to the numerical solution of the SCoTLASS
Computational Statistics & Data Analysis
RelaxMCD: Smooth optimisation for the Minimum Covariance Determinant estimator
Computational Statistics & Data Analysis
Editorial: 3rd Special issue on matrix computations and statistics
Computational Statistics & Data Analysis
Hi-index | 0.03 |
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.