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In this paper, a machine learning (ML) approach is presented that exploits accelerometers data to deal with gesture recognition (GR) problems. The proposed methodology aims at providing high accuracy classification for home automation systems, which are generally user independent, device independent, and device orientation independent, an heterogeneous scenario that has not been fully investigated in previous GR literature. The approach illustrated in this paper is composed of three main steps: event identification; feature extraction; and ML-based classification. The elements of the novelty of the proposed approach are 1) a preprocessing phase based on principal component analysis to increase the performance in real-world scenario conditions and 2) the development of parsimonious novel classification techniques based on sparse Bayesian learning. This methodology is tested on two datasets of four gesture classes (horizontal, vertical, circles, and eight-shaped movements) and on a further dataset with eight classes. In order to authentically describe a real-world home automation environment, the gesture movements are collected from more than 30 people who freely perform any gesture. It results in a dictionary of 12 and 20 different movements, respectively, in the case of the four-class and the eight-class databases. [ABSTRACT FROM AUTHOR]