Distance Transformation
=======================

Transforms distances in a dataset.

**Inputs**

- Distances: distance matrix

**Outputs**

- Distances: transformed distance matrix

The **Distances Transformation** widget is used for the normalization and inversion of distance matrices. The normalization of data is necessary to bring all the variables into proportion with one another.

![](images/DistanceTransformation-stamped.png)

1. Choose the type of [Normalization](https://en.wikipedia.org/wiki/Normalization_\(statistics\)):
   - **No normalization**
   - **To interval [0, 1]**
   - **To interval [-1, 1]**
   - [Sigmoid function](https://en.wikipedia.org/wiki/Sigmoid_function): 1/(1+exp(-X))
2. Choose the type of Inversion:
   - **No inversion**
   - **-X**
   - **1 - X**
   - **max(X) - X**
   - **1/X**
3. Produce a report.
4. After changing the settings, you need to click *Apply* to commit changes to other widgets. Alternatively, tick *Apply automatically*.

Example
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In the snapshot below, you can see how transformation affects the distance matrix. We loaded the *Iris* dataset and calculated the distances between rows with the help of the [Distances](../unsupervised/distances.md) widget. In order to demonstrate how **Distance Transformation** affects the [Distance Matrix](../unsupervised/distancematrix.md), we created the workflow below and compared the transformed distance matrix with the "original" one.

![](images/DistanceTransformation-Example.png)