Fuzzy Clustering for Finding Fuzzy Partitions of Many-Valued Attribute Domains in a Concept Analysis Perspective

Although an overall knowledge discovery process consists of a distinct pre-processing stage followed by the data mining step, it seems that existing formal concept analysis (FCA) and association rules mining (ARM) approaches, dealing with many-valued contexts, mainly focus on the data mining stage. An “intelligent” pre-processing of input contexts is often absent in existing FCA/ARM approaches, leading to an unavoidable information loss. Usually, many-valued attribute domains need to be first fuzzily partitioned. However, it is unrealistic that the most appropriate fuzzy partitions can be provided by domain experts. In this paper, an unsupervised learning stage, based on Fuzzy C-Means algorithm, is proposed in order to get fuzzy partitions that are faithful to data for quantitative attribute domains, and consequently for avoiding the loss of valuable association rules due to the use of empirical fuzzy partitions. More precisely, the paper reports an experiment where it is shown that some rules are no longer found because their support or confidence is too low when using such empirical partitions. Experimental results show that the learned fuzzy partition outperforms human expert fuzzy partitions. More generally, the paper provide discussions about the handling of many-valued attributes in both fuzzy FCA and fuzzy ARM. Keywords— Many-valued formal contexts, fuzzy partitions, fuzzy C-means, association rules.