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Development of smart grid technologies has created a promising atmosphere for smart cities and energy trading markets. Especially, traditional electricity consumers evolve into prosumers who produce as well as consume electricity in modern power electric systems. In this evolution, the electric power industry has tried to introduce the notion of local energy markets for prosumers. In the local energy market, prosumers purchase electricity from distributed energy generators or the other prosumers with surplus electricity via a local power exchange center. For this purpose, this paper proposes joint geometric clustering and truthful auction schemes in the local energy markets. The proposed clustering scheme is designed for distribution fairness of the distributed energy generator for serving prosumers, where the scheme is inspired by expectation and maximization based unsupervised learning. Moreover, this paper proposes an auction mechanism for truthful electricity trading in a local energy market. In order to guarantee truthful electricity trading, the proposed auction mechanism is constructed based on the Vickrey–Clarke–Groves auction, which was proven to guarantee truthful operations. The Hungarian method is also considered in addition to the auction. The simulation results for the auction verify that the utilities of local market energy entities are maximized when the prosumers are truthful. [ABSTRACT FROM AUTHOR]