Data vectors can be projected on the map by searching their BMUs. Since the map is ordered, nearby units will have similar data projected to them. By taking a set of data vectors and projecting them on the map a histogram is obtained with the value of the histogram for a map unit equaling the number of hits the map unit got from the data set. Different data sets can be easily compared by comparing these histograms, see for example figure 2.8.
Figure 2.8: Measurements from a computer system from two days depicted as a data set histogram. In (a) and (c) the value of the histogram at a map unit is depicted as different sized rectangles. The bigger the rectangle, the higher the histogram in that unit. The background in the figures is the u-matrix representation of the map. In (b) and (d) the same histograms are depicted as 3D-plots, where the height directly corresponds to the value of the histogram.
In time-dependent applications, trajectories are frequently used [19, 48]. A trajectory is the path which the projections, or the BMUs, of subsequent data vectors form on the map as shown in figure 2.9. In process monitoring, the clusters of the map correspond to process states, and by using the trajectory, the state and the history of the process can be easily visualized. It is also important to know how reliably the map has been able to analyze the input vector. For this the quantization error, or the distance, between the input vector and its BMU is normally used. Figure 2.10 shows one way to visualize the quantization error on a map.
Figure 2.9: Trajectory plotted on top of the u-matrix of a SOM. The arrows show the consecutive BMUs.
Figure 2.10: Visualization of quantization errors of two input vectors. The longer the pole, the bigger the quantization error. As the quantization error increases the head of the pole moves further away from the map plane.