| Author | Message | ||
     Donald J Dahm (djdahm) Advanced Member Username: djdahm Post Number: 23 Registered: 2-2007 |
In my opinion, the number of principle components (determinced by some sound statistical technique) would have a chance of being a reasonable representation of the "real" number of latent variables, except for the fact that the data we use is almost always non-linear and there are a bunch of additional components necessary to compensate for that. I will let the chemometic experts answer the rest of your questions, and while they ar at it, they can tell me why I am wrong. | ||
| Francisco Arteaga (francisco) New member Username: francisco Post Number: 1 Registered: 3-2009 |
Dear chemometricians, When we need to determine the number of principal components for estimate a PCA model from a data set X, there are a lot of procedures with more or less statistical foundament. My question is if this latent dimension is determined by the covariance matrix of X (different data sets with the same covariance matrix have the same latent dimension?), or if the latent dimension is determined by the eigenvalues of the covariance matrix (different covariance matrices can have the same set of eigenvalues). If I have a data set X, can I change X by other data set with the same covariance matrix (or with the same eigenvalues for the covariance matrix) in order to estimate the number of principal components? Some methods for determining the latent dimension are based on the eigenvalues for the covariance matrix (scree plot, broken stick, ...), and others are based on the data set (cross validation). Is there any method based directly on the covariance matrix? I wonder to what extent the latent dimension is a real property for a data set or it is only an useful (but problematic) invention. see you, Francisco |