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In this paper we address the issue of using local embeddings for data visualization in two and three dimensions, and for classification. We advocate their use on the basis that they provide an efficient mapping procedure from the original dimension of the data, to a lower intrinsic dimension. We depict how they can accurately capture the user's perception of similarity in high-dimensional data for visualization purposes. Moreover, we exploit the low-dimensional mapping provided by these embeddings, to develop new classification techniques, and we show experimentally that the classification accuracy is comparable (albeit using fewer dimensions) to a number of other classification procedures.