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The principles of similarity and proximity often work together to form a Visual Hierarchy. Either principle can dominate the other, depending on the application and combination of the two. For example, in the grid to the left, the similarity principle dominates the proximity principle; the rows are probably seen before the columns.
Thus, complex hypotheses must predict data much better than do simple hypotheses before researchers reject the simple hypotheses. Recent advances employ information theory, a close cousin of likelihood, which uses Occam's razor in the same way. The choice of the "shortest tree" relative to a not-so-short tree under any optimality criterion ...
Contour completion occurs in accordance with the Gestalt laws of grouping: similarity, closure, figure-ground, continuity and proximity. The automatic utilisation of Gestalt laws allows us to perceive these objects as separate, but does not provide a fully completed image of the occluded stimulus.
The Law of Similarity is employed by selecting similar map symbols for similar kinds of features or features with similar properties; the Law of Proximity is crucial to identifying geographic patterns and regions; and the Laws of Closure and Continuity allow users to recognize features that may be obscured by other features (such as when a road ...
From a spatial point of view, nearness (a.k.a. proximity) is considered a generalization of set intersection.For disjoint sets, a form of nearness set intersection is defined in terms of a set of objects (extracted from disjoint sets) that have similar features within some tolerance (see, e.g., §3 in).
Formally, if is a group and is a subset of , the normal closure of is the intersection of all normal subgroups of containing : [1] = .. The normal closure is the smallest normal subgroup of containing , [1] in the sense that is a subset of every normal subgroup of that contains .
Triadic closure is a concept in social network theory, first suggested by German sociologist Georg Simmel in his 1908 book Soziologie [Sociology: Investigations on the Forms of Sociation]. [1] Triadic closure is the property among three nodes A, B, and C (representing people, for instance), that if the connections A-B and A-C exist, there is a ...
In point-set topology, Kuratowski's closure-complement problem asks for the largest number of distinct sets obtainable by repeatedly applying the set operations of closure and complement to a given starting subset of a topological space. The answer is 14. This result was first published by Kazimierz Kuratowski in 1922. [1]