Fuzzy Logic and Applications

Cluster analysis of high-dimensional data has become of special interest in recent years. The term high-dimensional data can refer to a larger number of attributes – 20 or more – as they often occur in database tables. But high-dimensional data can also mean that we have to deal with thousands of attributes as in the context of genomics or proteomics data where thousands of genes or proteins are measured and are considered in some analysis tasks as attributes. A main reason, why cluster analysis of high-dimensional data is different from clustering low-dimensional data, is the concentration of norm phenomenon, which states more or less that the relative differences between distances between randomly distributed points tend to be more and more similar in higher dimensions. On the one hand, fuzzy cluster analysis has been shown to be less sensitive to initialisation than, for instance, the classical k-means algorithm. On the other, standard fuzzy clustering is stronger affected by the concentration of norm phenomenon and tends to fail easily in high dimensions. Here we present a review of why fuzzy clustering has special problems with high-dimensional data and how this can be amended by modifying the fuzzifier concept. We also describe a recently introduced approach based on correlation and an attribute selection fuzzy clustering technique that can be applied when clusters can only be found in lower dimensions.

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