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A common neural network used for complex data clustering is the Self Organizing Maps(SOM). This algorithm have a expensive training step, that occur mainly on high dimensional applications like image clustering. This makes impossible for some of these applications to be run in real time or even in a feasible time. On this paper we explore the use of GPUs with the NVIDIA CUDA language to decrease computational cost of SOM. We propose a three steps implementation able to reduce the computational complexity of the algorithm under SIMD paradigm and also making a good use of GPU's resources. At the end we were able to get a peak speed-up of 44 times against a C CPU implementation, fact that concludes about SOM's data parallelism.