Comparing datasets by attribute alignment

Metalearning approach to the model selection problem - exploiting the idea that algorithms perform similarly on similar datasets - requires a suitable metric on the dataset space. One common approach compares the datasets based on fixed number of features describing the datasets as a whole. The information based on individual attributes is usually aggregated, taken for the most relevant attributes only, or omitted altogether. In this paper, we propose an approach that aligns complete sets of attributes of the datasets, allowing for different number of attributes. By supplying the distance between two attributes, one can find the alignment minimizing the sum of individual distances between aligned attributes. We present two methods that are able to find such an alignment. They differ in computational complexity and presumptions about the distance function between two attributes supplied. Experiments were performed using the proposed methods and the results were compared with the baseline algorithm.