# PCATransform

This logic uses the result of the PCA logic (the eigenvectors) to transform images into a new space spanned by these eigenvectors. I.e. Images can be represented as factors of eigenvectors, a so called linear combination.

## Usage

Firstly PCA-transform can be used with any set of eigenvectors (as long as the x/y/z- dimensions of the PCA-input and the images used in the PCA transform are the same) to yield a set of linear factors. This is called a forward transform. Secondly, these linear factors can be used to generate images by multiplying eigenvectors and linear factors (back-transform).

## Modes/Processes

### Pca forward transform

Here, linear factors are calculated for a given set of INPUT images using the provided eigenvectors.

Parameters | Description |
---|---|

Desired Output | Lets you choose the kind of output. Linear factor vectors are just 1D plots of the linear factors per eigenvector as used in the back-transform. Images with linear factors as headerkeys just append the linear factors to the header. This is used as input for example the energy landscape calculation. |

### Pca backward transform

Here the linear factor vectors are used as INPUT. The eigenvectors times the linear factors gives you the original data (minus the amount of information you discarded by choosing the number of eigenvectors).

## Concept

Based on the eigenvectors calculated by PCA, this logic calculates linear factors or vice versa calculates “raw” images or volumes by using linear factors and the eigenvectors. However, by simply choosing low numbers of eigenvectors filtering through Dimensionality reduction can be done.