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Foundations of the Parafac Procedure: Models and Conditions for an 'Explanatory' Multi-Modal Factor Analysis.

PB197824

Publication Date	1970
Personal Author	Harshman, R. A.
Page Count	84
Abstract	Simple structure and other common principles of factor rotation do not in general provide strong grounds for attributing explanatory significance to the factors which they select. In contrast, it is shown that an extension of Cattell's principle of rotation to Proportional Profiles (PP) offers a basis for determining explanatory factors for three-way or higher order multi-mode data. Conceptual models are developed for two basic patterns of multi-mode data variation, system- and object-variation, and PP analysis is found to apply in the system-variation case. A series of tests, conducted with synthetic data of known factor composition, demonstrate the capabilities of linear and non-linear versions of the model, provide data on the minimal necessary conditions of uniqueness, and reveal the properties of the analysis procedures when these minimal conditions are not fulfilled. Three-mode PP factor analysis is applied to a three-way set of real data consisting of the fundamental and first three formant frequencies of 11 persons saying 8 vowels. A unique solution is extracted, consisting of three factors which are highly meaningful and consistent with prior knowledge and theory concerning vowel quality. (Author)
Keywords	Phonology Factor analysis Mathematical models
Source Agency	National Science Foundation
NTIS Subject Category	92D - Education, Law, & Humanities
Corporate Authors	California Univ., Los Angeles.
Document Type	Technical Report
Title Note	Working papers.
NTIS Issue Number	197108

Foundations of the Parafac Procedure: Models and Conditions for an 'Explanatory' Multi-Modal Factor Analysis.

Foundations of the Parafac Procedure: Models and Conditions for an 'Explanatory' Multi-Modal Factor Analysis.
PB197824

Publication Date	1970
Personal Author	Harshman, R. A.
Page Count	84
Abstract	Simple structure and other common principles of factor rotation do not in general provide strong grounds for attributing explanatory significance to the factors which they select. In contrast, it is shown that an extension of Cattell's principle of rotation to Proportional Profiles (PP) offers a basis for determining explanatory factors for three-way or higher order multi-mode data. Conceptual models are developed for two basic patterns of multi-mode data variation, system- and object-variation, and PP analysis is found to apply in the system-variation case. A series of tests, conducted with synthetic data of known factor composition, demonstrate the capabilities of linear and non-linear versions of the model, provide data on the minimal necessary conditions of uniqueness, and reveal the properties of the analysis procedures when these minimal conditions are not fulfilled. Three-mode PP factor analysis is applied to a three-way set of real data consisting of the fundamental and first three formant frequencies of 11 persons saying 8 vowels. A unique solution is extracted, consisting of three factors which are highly meaningful and consistent with prior knowledge and theory concerning vowel quality. (Author)
Keywords	Phonology Factor analysis Mathematical models
Source Agency	National Science Foundation
NTIS Subject Category	92D - Education, Law, & Humanities
Corporate Authors	California Univ., Los Angeles.
Document Type	Technical Report
Title Note	Working papers.
NTIS Issue Number	197108