Fig. 1. Basic structure of a data stream model.

Fig. 2. Data streams are compared within a sliding window of fixed size. In the example above, the behavior of the two streams is obviously quite different. In the example below, the two streams are similar to some extent.

Fig. 3. A window of length w is divided into m blocks of size v.

Fig. 4. Original (noisy) signal and DFT-filtered curve.

Fig. 5. Incremental version of the K-means algorithm for clustering data streams.

Fig. 6. A slight change of the data streams, here indicated as points, will usually not change the clustering structure drastically. In this example, the clusters before (light points) and after the modification (dark points) are even identical.

Fig. 7. Snapshots of a dynamic clustering structure at different time points (upper left to lower right).

Fig. 8. First online visualization tool.

Fig. 9. Second online visualization tool.

Fig. 10. Example of a prototypical data stream (solid line) and a distorted version (dashed line).

Fig. 11. Mean processing time per block and standard deviation for different numbers of DFT coefficients (increasing curve), average processing time and standard deviation for the original streams (horizontal lines).

Fig. 12. Average quality of the clustering structure for different numbers of DFT coefficients (1, 2, 10, 25).

Fig. 13. Average quality of the clustering structure for different numbers of blocks per window.

Fig. 14. Changing number of clusters over time.

Fig. 15. Three exemplary stock rates (deviation from the mean value) recorded between 04-05-14, 11:29 a.m. and 04-05-14, 3:44 p.m.

Fig. 16. Visualization of the hierarchical clustering structure (dendogram). Rows and columns correspond to stock rates. The darker a field is, the higher is the corresponding similarity degree.

Fig. 17. Distribution of similarity degrees, plotted in the form of a histogram together with the fitted normal distribution (smooth curve).

Notation