Deep learning techniques have been paramount in the last years, mainly due to their outstanding results in a number of applications. In this paper, we address the issue of fine-tuning parameters of Deep Belief Networks by means of meta-heuristics in which real-valued decision variables are described by quaternions. Such approaches essentially perform optimization in fitness landscapes that are mapped to a different representation based on hypercomplex numbers that may generate smoother surfaces. We therefore can map the optimization process onto a new space representation that is more suitable to learning parameters. Also, we proposed two approaches based on Harmony Search and quaternions that outperform the state-of-the-art results obtained so far in three public datasets for the reconstruction of binary images.
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