Fuzzy Clustering Via Proportional Membership ModelIOS Press, 2005 - 178 páginas Development of models with explicit mechanisms for data generation from cluster structures is of major interest in order to provide a theoretical framework for cluster structures found in data. Especially appealing in this regard are the so-called typological structures in which observed entities relate in various degrees to one or several prototypes. Such structures are relevant in many areas such as medicine or marketing, where any entity (patient/consumer) may adhere, with different degrees, to one or several prototypes (clinical scenario/consumer behavior), modelling a typological classification. In fuzzy clustering, the fuzzy c-means (FCM) method has become one of the most popular techniques. As a fuzzy analogue of c-means crisp clustering, FCM models a typological classification, much the same way as c-means. However, FCM does not adhere to the statistical paradigm at which the data are considered generated by a cluster structure, while crisp c-means does. The present work proposes a framework for typological classification based on a fuzzy clustering model of data generation. |
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3D projection analysis application AutoClass Bezdek c-partition space classification cluster prototypes cluster structure clustering algorithms clustering criterion clustering methods clustering model concept condition constraints convergence convex convex set criteria criterion function data mining data points data scatter data set defined density disorders data set Euclidean distance FCM and FCPM FCPM model FCPM-AE FCPM-m feature values Figure found by FCM fuzzy c-means fuzzy c-partition fuzzy clustering fuzzy set theory Fuzzy Systems gradient projection method high dimensional ideal type IEEE Transactions initialisation iterative Lipschitz continuity m-weight Mahalanobis distance matrix membership functions membership values mental disorders data Mirkin mixture model node number of clusters number of prototypes objective function optimal optimisation original prototypes parameters partitional clustering partitions found pattern recognition possibilistic probabilistic proportional membership prototypes found Section square-error criterion standardisation stepsize Table underlying types unsupervised learning updated v₁ variables vector weight contributions