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Symmetry 2018, 10(5), 133; https://doi.org/10.3390/sym10050133

Towards Generalized Noise-Level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

Nano-Crystallography Group, Department of Physics, Portland State University, Portland, OR 97207-0751, USA
Received: 29 January 2018 / Revised: 6 April 2018 / Accepted: 11 April 2018 / Published: 25 April 2018
(This article belongs to the Special Issue Mathematical Crystallography)
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Abstract

Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds or null hypothesis tests are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e., in all real-world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review. View Full-Text
Keywords: crystallographic symmetry classifications; geometric Akaike Information Criteria; Akaike weights; multi-model inference; information theory crystallographic symmetry classifications; geometric Akaike Information Criteria; Akaike weights; multi-model inference; information theory
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Moeck, P. Towards Generalized Noise-Level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns. Symmetry 2018, 10, 133.

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