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Assessing the similarity between cases is a key aspect of the retrieval phase in case-based reasoning (CBR). In most CBR work, similarity is assessed based on feature value descriptions of cases using similarity metrics, which use these feature values. In fact, it might be said that this notion of a feature value representation is a defining part of the CBR worldview-it underpins the idea of a problem space with cases located relative to each other in this space. Recently, a variety of similarity mechanisms have emerged that are not founded on this feature space idea. Some of these new similarity mechanisms have emerged in CBR research and some have arisen in other areas of data analysis. In fact, research on kernel-based learning is a rich source of novel similarity representations because of the emphasis on encoding domain knowledge in the kernel function. In this paper, we present a taxonomy that organizes these new similarity mechanisms and more established similarity mechanisms in a coherent framework.