Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Optinalysis: A New Method of Data Analysis and Comparison

Version 1 : Received: 3 August 2020 / Approved: 5 August 2020 / Online: 5 August 2020 (03:43:11 CEST)
Version 2 : Received: 12 September 2021 / Approved: 13 September 2021 / Online: 13 September 2021 (13:27:39 CEST)

How to cite: Abdullahi, K.B. Optinalysis: A New Method of Data Analysis and Comparison . Preprints 2020, 2020080072 (doi: 10.20944/preprints202008.0072.v2). Abdullahi, K.B. Optinalysis: A New Method of Data Analysis and Comparison . Preprints 2020, 2020080072 (doi: 10.20944/preprints202008.0072.v2).

Abstract

The key concepts in symmetry detection and similarity, identity measures are automorphism and isomorphism respectively. Therefore, methods for symmetry detection and similarity, identity measures should be functionally bijective, inverse, and invariance under a set of mathematical operations. Nevertheless, few or no existing method is functional for these properties. In this paper, a new methodological paradigm, called optinalysis, is presented for symmetry detections, similarity, and identity measures between isoreflective or autoreflective pair of mathematical structures. The paradigm of optinalysis is the re-mapping of isoreflective or autoreflective pairs with an optical scale. Optinalysis is characterized as invariant under a set of transformations and its isoreflective polymorphism behaves on polynomial and non-polynomial models.

Keywords

Autoreflectivity; Identity; Isoreflectivity; Kabirian coefficient; Similarity; Symmetry

Subject

MATHEMATICS & COMPUTER SCIENCE, Numerical Analysis & Optimization

Comments (1)

Comment 1
Received: 13 September 2021
Commenter: Kabir Bindawa Abdullahi
Commenter's Conflict of Interests: Author
Comment: The previous version of the manuscript has been revised for the following:
1. Grammer checked.
2. Further details and clarifications on the concept of optinalysis.
2. Sections were re-structured and edited.
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