Shafronenko, A. Yu.Bodyanskiy, Ye. V.Rudenko, D. A.2020-11-162020-11-162020Shafronenko, A., Bodyanskiy, Ye., Rudenko, D. Adaptive Neuro-Fuzzy Methods for Distorted Data Clustering. Saarbrücken, LAP LAMBERT Academic Publishing, 2020.http://openarchive.nure.ua/handle/document/13809The problem of data sets described by vector-images clustering often occurs in many applications associated with Data Mining [40, 41], when processed vector-image with different levels of probabilities, possibilities or memberships, can belong to more than one class. However, there are situations when the data sets contain missing values. In this situation more effective is to use mathematical apparatus of Computational Intelligence [Rutkowski, 2008] and, first of all artificial neural networks [8], that solve task of restoring the lost observations and modifications of the popular method of fuzzy c-means [22], which solve the problem of clustering without recovery of data. Existing approaches for data processing with missing values [6], are efficient in cases when the massive of the original observations is given in batch form and does not change during the processing. At the same time, there is a wide class of problems in which the data that arrive to the processing, have the form of sequence that is feed in real time as it occurs in the training of Kohonen self-organizing maps [1] or their modifications [2]. In this regard we have introduced [42] the adaptive neuro-fuzzy Kohonen network to solve the problem of clustering data with gaps based on the strategy of partial distances (PDS FCM). However, in situations where the number of such missing values is too big, the strategy of partial distances may be not effective, and therefore it may be necessary, along with the solution of fuzzy clustering simultaneously estimate the missing observations. In this situation, a more efficient is approach that is based on the optimal expansion strategy (OCS FCM) [22]. This chapter is devoted to the task of on-line data clustering using the optimal expansion strategy, adapted to the case when information is processed in a sequential mode, and its volume is not determined in advance.enFuzzy clusteringdata with gapsmachine learningprobabolistic fuzzy clusteringBook chapter