Differential privacy for learning vector quantization

Prototype-based machine learning methods such as learning vector quantisation (LVQ) offer flexible classification tools, which represent a classification in terms of typical prototypes. This representation leads to a particularly intuitive classification scheme, since prototypes can be inspected by a human partner in the same way as data points. Yet, it bears the risk of revealing private information included in the training data, since individual information of a single training data point can significantly influence the location of a prototype. In this contribution, we investigate the question how to algorithmically extend LVQ such that it provably obeys privacy constraints as offered by the notion of so-called differential privacy. More precisely, we demonstrate the sensitivity of LVQ to single data points and hence the need of its extension to private variants in case of possibly sensitive training data. We investigate three technologies which have been proposed in the context of differential privacy, and we extend these technologies to LVQ schemes. We investigate the effectiveness and efficiency of these schemes for various data sets, and we evaluate their scalability and robustness as regards the choice of meta-parameters and characteristics of training sets. Interestingly, one algorithm, which has been proposed in the literature due to its beneficial mathematical properties, does not scale well with data dimensionality, while two alternative techniques, which are based on simpler principles, display good results in practical settings. (C) 2019 Published by Elsevier B.V.