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Traditional machine learning and pattern recognition techniques are intimately linked to the notion of "feature space." Adopting this view, each object is described in terms of a vector of numerical attributes and is therefore mapped to a point in a Euclidean (geometric) vector space so that the distances berween the points reflect the observed (dis)similarities berween the respective objects. This kind of representation is attractive because geometric spaces offer powerful analytical as well as computational tools that are simply not available in other representations. However, the geometric approach suffers from a major intrinsic limitation which concerns the representational power of vectorial, feature-based descriptions. In fact, there are numerous application domains where either it is not possible to find satisfactory features or they are inefficient for learning purposes. By departing from vector-space representations one is confronted with the challenging problem of dealing with (dis)similarities that do not necessarily possess the Euclidean behavior or not even obey the requirements of a metric. The lack of "(geo)metric" (i.e., geometric and/or metric) properties undermines the very foundations of traditional machine learning theories and algorithms, and poses totally new theoretical/ computational questions and challenges that the research community is currently trying to address. The goal of the special issue is to consolidate research efforts in this area by soliciting and publishing high-quality papers which, together, will present a clear picture of the state of the art. We encourage submissions of papers addressing theoretical, algorithmic, and practical issues related to the rwo fundamental questions that arise when abandoning the realm of vectorial, feature-based representations, namely: (1) how can one obtain suitable similarity information from data representations that are more powerful than, or simply different from, the vectorial? (2) how can - ne use similarity information in order to perform learning and classification tasks? We aim at covering a wide range of problems and perspectives, from supervised to unsupervised learning, from generative to discriminative models, and from theoretical issues to real-world applications.