On the need for metrics in dictionary learning assessment

Dictionary-based approaches are the focus of a growing attention in the signal processing community, often achieving state of the art results in several application fields. Albeit their success, the criteria introduced so far for the assessment of their performances suffer from several shortcomings. The scope of this paper is to conduct a thorough analysis of these criteria and to highlight the need for principled criteria, enjoying the properties of metrics. Henceforth we introduce new criteria based on transportation like metrics and discuss their behaviors w.r.t the literature.