# wmspca

Multiscale principal component analysis

## Syntax

## Description

`[`

returns a simplified version `xsim`

,`qual`

,`npc_out`

,`decsim`

,`pca_params`

] = wmspca(`x`

,`level`

,`wname`

,`npc_in`

)`xsim`

of the input matrix
`x`

obtained from the wavelet-based multiscale principal component analysis
(PCA). The wavelet decomposition is performed using the decomposition level
`level`

and the wavelet `wname`

.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

The multiscale principal components generalizes the usual PCA of a multivariate signal seen as a matrix by performing simultaneously a PCA on the matrices of details of different levels. In addition, a PCA is performed also on the coarser approximation coefficients matrix in the wavelet domain as well as on the final reconstructed matrix. By selecting conveniently the numbers of retained principal components, interesting simplified signals can be reconstructed.

## References

[1] Bakshi, Bhavik R. “Multiscale PCA
with Application to Multivariate Statistical Process Monitoring.” *AIChE
Journal* 44, no. 7 (July 1998): 1596–1610. https://doi.org/10.1002/aic.690440712.

## Version History

**Introduced in R2006b**