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This paper proposes a novel model that integrates the SOM (Self-Organizing Map) neural network and the kMER (kernel-based Maximum Entropy learning Rule) algorithm for data visualization and classification. The rationales and algorithm development of SOM-kMER are elaborated. Applicability of the proposed model is evaluated using a number of simulated and benchmark data sets. The outcomes demonstrate that SOM-kMER is able to achieve a faster convergence rate (as compared with the kMER) and produce visualization with fewer dead units (as compared with the SOM). The proposed SOM-kMER model is also able to form an equiprobabilistic map at the end of its learning process. On benchmark experiments, SOM-kMER achieves favourable results as compared with the SOM and other machine learning algorithms.