The Boolean algebra is, perhaps, the most well known dioid, and there exist Boolean matrix factorization algorithms that produce low reconstruction errors. In this thesis, however, a different objective function is used -- the description length of the data, which enables us to obtain more compact and highly interpretable results.
The tropical and subtropical algebras are much less known in the data mining field. While they find applications in areas such as job scheduling and discrete event systems, they are virtually unknown in the context of data analysis. We will use them to obtain idempotent nonnegative factorizations that are similar to NMF, but are better at separating most prominent features of the data.