Multi-Core Parallel Gradual Pattern Mining Based on Multi-Precision Fuzzy Orderings

Gradual patterns aim at describing co-variations of data such as the higher the size, the higher the weight. In recent years, such patterns have been studied more and more from the data mining point of view. The extraction of such patterns relies on efficient and smart orderings that can be built among data, for instance, when ordering the data with respect to the size, then the data are also ordered with respect to the weight. However, in many application domains, it is hardly possible to consider that data values are crisply ordered. When considering gene expression, it is not true from the biological point of view that Gene 1 is more expressed than Gene 2, if the levels of expression only differ from the tenth decimal. We thus consider fuzzy orderings and fuzzy gamma rank correlation. In this paper, we address two major problems related to this framework: (i) the high memory consumption and (ii) the precision, representation and efficient storage of the fuzzy concordance degrees versus the loss or gain of computing power. For this purpose, we consider multi-precision matrices represented using sparse matrices coupled with parallel algorithms. Experimental results show the interest of our proposal.