The U-Matrix is a representation of a self organizing map (SOM) where the Euclidean distance

Euclidean distance

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" distance between two points that one would measure with a ruler, and is given by the Pythagorean formula. By using this formula as distance, Euclidean space becomes a metric space...

between the codebook vector of the neighboring neurons is depicted in a gray scale image. It is used to visualize the data in a high dimensional space on a 2-D image.

Construction procedure

Once the SOM is trained using the input data, it is expected that the final map does not have any twists. In such a case the distance between the neighboring neurons gives an approximation of the distance between different parts of the underlying data. When such distances are depicted in a gray scale image, light colors depict the closely spaced nodes and darker colors indicate the more distant nodes. Thus, groups of light colors can be considered as a clusters, and the dark parts as the boundary regions. This way of representation can help us in visualizing the clusters in the high dimensional spaces.

Darker regions indicate that the distance between the nodes is large and lighter regions indicate that the codebook vectors are close. The clusters are separated by the dark gaps. This gives the details about the number of clusters in the data without any human intervention, such as in an unsupervised manner.