Social media is revealing itself as one of the main actors in the economic and social revolution we are currently witnessing, and in which the main factors are data and immediacy. Social media is producing a large amounts of data day by day, but this data is of no use unless it is processed for extracting relevant information from it. The efficient analysis of this immensity of data is mandatory to translate these mere data into information applicable to multiple areas. There are many techniques to deal with this problem, but undoubtedly one of the most useful techniques to extract meaningful knowledge from these data has been the clustering algorithms. However, clustering algorithms are cost-intensive from a computational point of view, especially when dealing with large data sets, and therefore require computing resources that offer high performance, which leads to another factor that must be taken into account for the efficient processing of this information, high performance computing. In this article, we show both points of view, the algorithmic one, applying several of the mentioned clustering algorithms, and on the other hand, preparing those algorithms to be executed in high performance computing platforms. Specifically in the article we present tests for the execution of the k-means, FM, and FCM algorithms in CPU and GPU, offering results in terms of efficiency of these algorithms. The results obtained show that an efficient implementation of these algorithms achieve speeds-up of 24x in some scenarios always taking advantage of GPUs.