Abstract - We use an information-theoretic criterion to assess the goodness-of-fit of the output of archetypal analysis (AA), also intended as a fuzzy clustering tool. It is an adaptation of an existing AIC-like measure to the specifics of AA. We test its effectiveness using artificial data and some data sets arising from real life problems. In most cases, the results achieved are similar to those provided by an external similarity index. The average reconstruction accuracy is about 93\%.
Abstract - Fuzzy c-means (FCM) clustering is known to be sensitive to outliers and noise. Possibilistic c-means (PCM) has been reported to be more robust against outliers and noise but may yield coincident clusters. We introduce a variant of PCM called sequential possibilistic one-means (SP1M) that finds clusters sequentially, takes into account the previously found clusters for initialization, and discards coincident clusters. Experiments with the well-known BIRCH benchmark data set and two variants of BIRCH indicate that SP1M is able to find a significantly larger percentage of the clusters contained in the data, with about twice as many cluster update steps, but significantly faster than FCM and PCM.
Abstract - The ideal type model by Mirkin and Satarov (1990) expresses data points as convex combinations of some `ideal type' points. However, this model cannot prevent the ideal type points being far away from the observations and, in fact, requires that. Archetypal analysis by Cutler and Breiman (1994) and proportional membership fuzzy clustering by Nascimento et al. (2003) propose different ways of avoiding this entrapment. We propose one more way out -- by assuming the ideal types being mutually orthogonal and transforming the model by multiplying it over its transpose. The obtained additive fuzzy clustering model for relational data is akin to that more recently analysed by Mirkin and Nascimento (2012) in a different context. The one-by- one clustering approach to the ideal type model is reformulated here as that naturally leading to a spectral clustering algorithm for finding fuzzy membership vectors. The algorithm is proven to be computationally valid and competitive against popular relational fuzzy clustering algorithms.
Abstract - This paper presents SS-MVFCVSMdd, a semi-supervised multiview fuzzy clustering algorithm for relational data described by multiple dissimilarity matrices. SS-MVFCVSMdd provides a fuzzy partition in a predetermined number of fuzzy clusters, a representative for each fuzzy cluster, learns a relevance weight for each dissimilarity matrix, and takes into account pairwise constraints must-link and cannot-link, by optimizing a suitable objective function. Experiments with multi-view real-valued data sets described by multiple dissimilarity matrices show the usefulness of the proposed algorithm.