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Relationships between higher‐order data array configurations and problem formulations in multivariate data analysis
Author(s) -
Esbensen Kim. H.,
Wold Svante,
Geladi Paul
Publication year - 1989
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1180030106
Subject(s) - multivariate statistics , data mining , curse of dimensionality , computer science , class (philosophy) , bilinear interpolation , data type , data analysis , data classification , variable (mathematics) , multivariate analysis , pattern recognition (psychology) , mathematics , artificial intelligence , statistics , machine learning , mathematical analysis , programming language
A scaffold for detailed understanding of the concept ‘dimensionality’ in data analysis is furnished by a systematic classification of higher‐order data array configurations. Three major types of problem formulation in multivariate data analysis can be characterized for relevant data classes : 1 data description (intra‐class data structure modelling of inter‐object and inter‐variable relationships) 2 classification (inter‐class discrimination) 3 correlation , regression (inter‐variable relationships).The relationship between these three categories of data analytical problem formulation and the fundamental data array classification is exposed. These relations are augmented to include the general case of data arrays of order R , and R ‐way data analysis with the use of bilinear projections is presented. Based upon this, some possible directions for the future development of data analysis may be imagined.