Rexel sente3/5/2023 The multi-class approach is more efficient because it matches feature points only if they are from the same class. We also introduce a new variant of the Hausdorff fraction similarity measure based on a multi-class approach, which we call the Multi-class Hausdorff Fraction (MCHF). In this paper, we adapt the above method to the set of similarity transformations. This method has been applied to problems involving translations, translation and scale, and Affine transformations. Recently, a new image registration method, based on the Hausdorff fraction and a multi-resolution search of the transformation space, has been developed in the literature. We show that our extension preserves the nice metric properties of the finite case, and finally provide some useful numerical examples that arise in EMO. In particular, this extension applies to bounded subsets of R k endowed with the Euclidean metric, which is the natural context for EMO applications. In this paper, we extend Δ p, q to a continuous function between general bounded subsets of finite measure inside a metric measure space. Later on, the two-parameter indicator Δ p, q has been proposed for finite sets as an extension to Δ p which also averages distances, but which yields some desired metric properties. As a remedy in the context of evolutionary multi-objective optimization (EMO), the averaged Hausdorff distance Δ p has been proposed that is better suited as an indicator for the performance assessment of EMO algorithms since such methods tend to generate outliers. For the approximation of certain objects via stochastic search algorithms this distance is, however, of limited use as it punishes single outliers. The Hausdorff distance is a widely used tool to measure the distance between different sets. Finally, we discuss a collection of examples and numericalresults obtained for the discrete and continuous incarnations of these distances that allow for anevaluation of their usefulness in concrete situations and for some interesting conclusions at the end,justifying their use and further study. Illustration of these resultsin particular situations are also provided. Among the presented results, we highlight the rigorousconsideration of metric properties of these definitions, including a proof of the triangle inequalityfor distances between disjoint subsets when p, q ≥ 1, and the study of the behavior of associatedindicators with respect to the notion of compliance to Pareto optimality. The presentation treats separately the definitions of the (p, q)-distances GDp,q, IGDp,q, and Δp,q for finite sets and their generalization for arbitrary measurable sets that covers as an importantexample the case of continuous sets. This new approach is expected to enhance our knowledge of the role of retrieval flexibility in creativity from a dynamic perspective.Ī brief but comprehensive review of the averaged Hausdorff distances that have recentlybeen introduced as quality indicators in multi-objective optimization problems (MOPs) is presented.First, we introduce all the necessary preliminaries, definitions, and known properties of thesedistances in order to provide a stat-of-the-art overview of their behavior from a theoretical pointof view. Retrieval flexibility mediated the links between the lifetime of the related brain state and creativity. The flexible functional connectivity within and between default mode, executive control, and salience provides further evidence on brain dynamics of creativity. Moreover, high flexibility was associated with the lifetime of a specific brain state during rest, characterized by interactions among large-scale cognitive brain systems. Our findings showed that retrieval flexibility was positively correlated with multiple creativity-related behavior constructs and can promote distinct search patterns in different creative groups. We developed 5 metrics to quantify retrieval flexibility based on previous studies, which confirmed the important role of creativity. This study aimed to capture different dynamic aspects of retrieval processes and examine the behavioral and neural associations between retrieval flexibility and creativity. However, there is insufficient research on how flexible memory retrieval acts on creative activities. The associative theory of creativity posits flexible retrieval ability as an important basis for creative idea generation. Creativity, the ability to generate original and valuable products, has long been linked to semantic retrieval processes.
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