## Principal component analysis (PCA)

Purpose

Description

Tips

Macro Synopsis

Modules

Related Functions

References

### Purpose

Principal component analysis

### Description

This function resembles the Karhunen-Loeve-Transform which
is often used in the field of image processing.
It performs an orthogonal base transformation of the input to obtain
data with maximum decorrelation of the channels,
thus exhibiting the essential properties and patterns of the multi-channel
signal x in the output signal y.

"Principal component analysis (PCA)" takes one parameter:

- Maximum relative error
`mre`, which is a sort of threshold
for the components (eigenvalues) of the singular value decomposition
that are taken into account.
Only the first q components, belonging to the largest eigenvalues
(given in descending order), are output in the resulting
multi-channel signal. The sum of the residual p-q eigenvalues, divided
by the sum of all eigenvalues, is guaranteed to be lower than `mre`.

There is message window output consisting of the eigenvalues of the covariance
matrix, the real error and the transformation matrix.
The output signal is of multi-channel type with q channels.

### Tips

If the relative error threshold `mre` is set to zero, the decomposition is carried out completely, and the full information of x will be covered. This is equivalent to a Karhunen-Loeve transform.

### Macro Synopsis

`y = PCA(x,mre);`

signal x,y;

float mre;

### Modules

Statistics

### Related Functions

Box-Cox transform, Detrended fluctuation analysis (DFA),
Exponential regression, Linear regression, Long term correlation analysis (LTCA),
Multilinear regression, Power regression,
R/S statistics, Remove DC,
Remove trend.
There is also a Dataplore ® macro 'Karhunen-Loeve-Transformation' (KLTrafo.dpm).

### References

Karhunen [52], Loeve [53]