One of the most significant current challenges in large-scale online socialnetworks, is to establish a concise and coherent method able to collect andsummarize data. Sampling the content of an Online Social Network (OSN) plays animportant role as a knowledge discovery tool. It is becoming increasingly difficult to ignore the fact that currentsampling methods must cope with a lack of a full sampling frame i.e., there isan imposed condition determined by a limited data access. In addition, anotherkey aspect to take into account is the huge amount of data generated by usersof social networking services. This type of conditions make especiallydifficult to develop sampling methods to collect truly reliable data.Therefore, we propose a low computational cost method for sampling emergingglobal trends on social networking services such as Twitter. The main purpose of this study, is to develop a methodology able to carry outan efficient collecting process via three random generators: Brownian, Illusionand Reservoir. These random generators will be combined with aMetropolis-Hastings Random Walk (MHRW) in order to improve the samplingprocess. We demonstrate the effectiveness of our approach by correctlyproviding a descriptive statistics of the collected data. In addition, we alsosketch the collecting procedure on real-time carried out on Twitter. Finally,we conclude with a trend concentration graphical description and a formalconvergence analysis to evaluate whether the sample of draws has attained anequilibrium state to get a rough estimate of the sample quality.
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