randomized databases at least for all of the 50 top-ranked tiles for which data is shown in these plots. This corroborates that the top-ranked tiles are indeed meaningful and cannot be attributed to randomness.

![0_image_0.png](0_image_0.png)

We believe that the true assessment of a subjective measure should be the subjective one provided just above. Still, we also conducted an **objective** comparison between our interestingness measure and the tiling method from Geerts et al (2004). We took each of the 3 abstract databases and artificially embedded large tiles in these databases by appending k **rows ('documents') as**
well as k columns ('words') to it, ensuring that the database cells in the intersection of the k new rows and the k **new columns are all equal to 1. To ensure that**
the overall statistics of the database are maintained, we furthermore randomly added ones in the cells in the intersection of the existing columns and the new rows, so as to ensure that the column densities remain the same. Similarly, we randomly added ones to the cells in the intersection of the existing rows and new columns to ensure the row frequencies are unchanged. We did this for various tile sizes k, namely for k = 5, 10, 15, **and 20.**
We then computed a ranking of tiles based on our newly proposed compression ratio interestingness measure, as well as based on the surface of a tile
(Geerts et al, 2004). We then compared the rank of the embedded **tile (or if**
possible a larger one containing it) in the ranking returned by these two interestingness measures. The results, shown in Table 5, clearly demonstrate that our proposed approach is much more effective in finding the embedded tile.

## 8 Conclusions

A significant amount of data mining research has been devoted to the assessment of data mining results when contrasted to prior information, leading **to the** notion of subjective measures of interestingness. A key task in this endeavour is the formalization of prior information.