Open AccessA dynamical-scanning inner product based on Euclidean inner product
Author(s) -
Ray-Ming Chen
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1592/1/012064
Subject(s) - product (mathematics) , euclidean geometry , construct (python library) , dot product , relation (database) , inner product space , euclidean distance , function (biology) , computer science , dynamical systems theory , mathematics , series (stratigraphy) , matrix (chemical analysis) , pure mathematics , artificial intelligence , geometry , data mining , physics , paleontology , materials science , quantum mechanics , evolutionary biology , biology , composite material , programming language
Euclidean dot product plays an important role in data analysis and relation comparison for its intuitive properties. However, for some complicated structures, for example, time series, it would be insufficient to construct a complete theory via this product. In order to resolve and accommodate these issues, we devise a dynamical-scanning inner product which would take the interaction, in particular in the sense of time shift, between two vectors into consideration and yield a relation that contains much more information. Though this device is based on Euclidean dot product, it is more much suitable and flexible for handling some complicated mathematical objects. In addition, we also construct a dynamical-scanning inner product for function spaces. In the end, we show how to apply our devices on both matrix representations and time series. These exploration might delve into some intrinsic properties of some mathematical concepts or models.