# ADICOV

Approximation of a DIstribution for a given COVariance (ADICOV) is a method that performs a constrained least squares approximation that is solved for any projection subspace, including that of Principal Component Analysis (PCA) and Partial Least Squares (PLS).

ADICOV approximates a data set by another data set with constrained covariance. This may be applied with two different goals: a) to simulate data with a specific covariance structure and space distribution and b) to test whether a data set satisfies the covariance structure in a projection model. Regarding goal a), ADICOV is the core of the simuleMV routine in the MEDA Toolbox. Regarding goal b), ADICOV can be employed for covariance-based Multivariate Statistical Process Control, like in the Figure. Covariance-based MSPC presents some interesting differences to standard MSPC, for instance it is more suitable for Big Data monitoring.

Other potential applications, yet to be considered, are model selection, model validation and classification.

#### Related references:

- Camacho, J., Padilla, P., Díaz-Verdejo, J., Smith, K., Lovett, D. Least-squares approximation of a space distribution for a given covariance and latent sub-space. Chemometrics and Intelligent Laboratory Systems, 2011, 105 (2): 171-180.