A New Approach to Constructing Maximal Consistent Blocks for Mining Incomplete Data

Handling the Complexity of Computing Maximal Consistent Blocks

“…The idea of the sequential update of the set of maximal consistent blocks based on Property 5 from [16] proposed in [25] is more effective than the commonly used method of constructing the blocks. However, the subsets merging, which removes subsets by performing comparisons between two sets (the current set of maximal consistent blocks obtained so far and the new one built for the next attribute), has a significant impact on the overall performance.…”

“…In practice, however, the efficiency is reduced by the fact that p − 1 processes have to wait for the processes executing the slowest task in a batch. Therefore, in the worst case, the relative improvement compared to the sequential algorithm is O(n n For the demonstration of the real values of the efficiency, the abalone data set with all missing attribute values interpreted as "do not care" conditions was selected, due to the fact that during the experiments performed, using the sequential algorithm, this set turned out to be the most demanding one [25]. The analysis was conducted using 4, 6, 8, 12, 16, 20 and 32 processors.…”

“…Firstly, the obtained blocks might not be maximal, especially for data sets for which a characteristic relation is not transitive. The second problem is that, in some cases, the reported computational complexity of the algorithms is underestimated [25]. Additionally, in papers [18,26], during the comparison of characteristic sets with generalized maximal consistent blocks in terms of an error rate and complexity of induced rule sets, the authors suggested that characteristic sets can be computed in polynomial time, while computing maximal consistent blocks is associated with exponential time complexity for incomplete data with "do not care" conditions.…”