md`The U-Matrix is a common and useful way to represent SOM 2D maps. Using the means of distance to each neighbours (using hexagons so a neuron has at maximum 6 neighbours), we can display a grey scale of density. Darker neurons are isolated and brighter are densily grouped. The U-Matrix represents unlabelled neurons, showing borders between areas. It's not always easy to interpret the results of such a map but some clusters are emerging. As [Vega](https://vega.github.io/vega/docs/transforms/) allows a lot of transformation on data, I choose to implement the umatrix calculation directly in the specification. The visualisation takes a list of neurons as an input containing the x and y coodinates of the neuron and its vector (as an array). The specification will normalize the data and calculates the mean of distance for each hexagonal neighbour. Additionaly to the current_step, autoplay and scale, that have been used in other visualizations, are now the following inputs: - visualization allows to select between **iso**, **umatrix** and **classes** visualizations: - **iso** shows the distances using isocontours - **usmatrix** is the U-Matrix - **classes** displays the labelled neuron map - umatrixScheme allows to select between a grey scale and a blue-green scale - umatrixInverted allows to invert the scale (dark neurons are close to each other and bright are isolated) The current visualization is displaying the same data that the [SOM 2](#som_2) visualization. We can see that: - **iso** representation and **umatrix** are displaying the same information in different styles - The Iris-setosa class is clearly separated from the others - The Iris-versicolor and Iris-virginica are not clearly emerging from the U-Matrix - In **classes** representation, when multiples classes are activating the node, the size of second class border is proportional to the number of entries of the dominant class. We can then directly watch the most 'confusing' nodes `