The 3W Model and Algebra for Unified Data Mining

Real data mining/analysis applications call for a framework which adequately supports knowledge discovery as a multi-step process, where the input of one mining operation can be the output of another. Previous studies, primarily focusing on fast computation of one speci c mining task at a time, ignore this vital issue. Motivated by this observation, we develop a unied model supporting all major mining and analysis tasks. Our model consists of three distinct worlds, corresponding to intensional and extensional dimensions, and to data sets. The notion of dimension is a centerpiece of the model. Equipped with hierarchies, dimensions integrate the output of seemingly dissimilar mining and analysis operations in a clean manner. We propose an algebra, called the dimension algebra, for manipulating (intensional) dimensions, as well as operators that serve as \bridges" between the worlds. We demonstrate by examples that several real data mining processes can be captured using our model and algebra. We demonstrate the naturality of the algebra by establishing several identities. Finally, we discuss e cient implementation of the proposed framework.