Possibilistic and fuzzy clustering methods for robust analysis of non-precise data

This work focuses on robust clustering of data affected by imprecision. The imprecision is managed in terms of fuzzy sets. The clustering process is based on the fuzzy and possibilistic approaches. In both approaches the observations are assigned to the clusters by means of membership degrees. In fuzzy clustering the membership degrees express the degrees of sharing of the observations to the clusters. In contrast, in possibilistic clustering the membership degrees are degrees of typicality. These two sources of information are complementary because the former helps to discover the best fuzzy partition of the observations while the latter reflects how well the observations are described by the centroids and, therefore, is helpful to identify outliers. First, a fully possibilistic k-means clustering procedure is suggested. Then, in order to exploit the benefits of both the approaches, a joint possibilistic and fuzzy clustering method for fuzzy data is proposed. A selection procedure for choosing the parameters of the new clustering method is introduced. The effectiveness of the proposal is investigated by means of simulated and real-life data

Applying subclustering and Lp distance in Weighted K-Means with distributed centroids

We consider the Weighted K-Means algorithm with distributed centroids aimed at clustering data sets with numerical, categorical and mixed types of data. Our approach allows given features (i.e., variables) to have different weights at different clusters. Thus, it supports the intuitive idea that features may have different degrees of relevance at different clusters. We use the Minkowski metric in a way that feature weights become feature re-scaling factors for any considered exponent. Moreover, the traditional Silhouette clustering validity index was adapted to deal with both numerical and categorical types of features. Finally, we show that our new method usually outperforms traditional K-Means as well as the recently proposed WK-DC clustering algorithm.Peer reviewe

A Survey of Adaptive Resonance Theory Neural Network Models for Engineering Applications

This survey samples from the ever-growing family of adaptive resonance theory (ART) neural network models used to perform the three primary machine learning modalities, namely, unsupervised, supervised and reinforcement learning. It comprises a representative list from classic to modern ART models, thereby painting a general picture of the architectures developed by researchers over the past 30 years. The learning dynamics of these ART models are briefly described, and their distinctive characteristics such as code representation, long-term memory and corresponding geometric interpretation are discussed. Useful engineering properties of ART (speed, configurability, explainability, parallelization and hardware implementation) are examined along with current challenges. Finally, a compilation of online software libraries is provided. It is expected that this overview will be helpful to new and seasoned ART researchers