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Cosine similarity is a widely used measure of the relatedness of pre-trained word embeddings, trained on a language modeling goal. Datasets such as WordSim-353 and SimLex-999 rate how similar words are according to human annotators, and as such are often used to evaluate the performance of language models. Thus, any improvement on the word similarity task requires an improved word representation. In this paper, we propose instead the use of an extended cosine similarity measure to improve performance on that task, with gains in interpretability. We explore the hypothesis that this approach is particularly useful if the word-similarity pairs share the same context, for which distinct contextualized similarity measures can be learned. We first use the dataset of Richie et al. (2020) to learn contextualized metrics and compare the results with the baseline values obtained using the standard cosine similarity measure, which consistently shows improvement. We also train a contextualized similarity measure for both SimLex-999 and WordSim-353, comparing the results with the corresponding baselines, and using these datasets as independent test sets for the all-context similarity measure learned on the contextualized dataset, obtaining positive results for a number of tests.