Membership embedding space approach and spectral clustering

The data representation strategy termed "Membership Embedding" is a type of similarity-based representation that uses a set of data items in an input space as reference points (probes), and represents all data in terms of their membership to the fuzzy concepts represented by the probes. The technique has been proposed as a concise representation for improving the data clustering task. In this contribution, it is shown that this representation strategy yields a spectral clustering formulation, and this may account for the improvement in clustering performance previously reported. Then the problem of selecting an appropriate set of probes is discussed in view of this result.