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Recently, the community has shown a growing interest in building online learning models. In this paper, we are interested in the framework of fuzzy equivalences obtained by residual implications. Models are generally based on the relevance degree between pairs of objects of the learning set, and the update is obtained by using a standard stochastic (online) gradient descent. This paper proposes another method for learning fuzzy equivalences using a Quasi-Newton optimization. The two methods are extensively compared on real data sets for the task of nearest sample(s) classification. [ABSTRACT FROM PUBLISHER]