This paper presents an alternative to the traditional impedance based fault location methods, using a simple technique of the learning approaches called k-Nearest Neighbors (k-NN), where besides the fault location distance, the multiple estimation problem is also addressed. This approach only uses the single end measurements of voltage and current available at the power substation. As principal advantage, considering the classical approaches, this alternative has not dependency on the power system model and also considers the spacial characteristics of the distribution systems. Furthermore, the multiple estimation problem, typical of all fault location approaches, is addressed. According to the proposed tests, faults location in different nodes and values of fault resistances are successfully determined, having an average error rate lower than 1.5% and 13% in distance estimation and zone identification respectively.