A measure of well-defined homogenous subsets among indicator variables on which multivariate data is generated is given by Kaiser-Meier-Olkin’s measure of sampling adequacy (KMO). This measure relies on a subtle use of a cut-off value. This cut-off value as well as the expected number of dimensions in the data constitute important background information for dimensionality detection that is not reported in the application of dimensionality reduction techniques. The implication is that these techniques do not establish a priori the existence of dimensionality in the data, and hence could be misapplied. In this regard, the study proposes an automated threshold-setting approach with an algorithm that generates a data-specific optimal threshold from the data structure for detecting the dimensionality of multivariate data for more accurate results. Three different threshold settings are implemented for various correlation profiles of the data. The known techniques may now be useful for purposes of interpretation of the extracted reduced dimensions. Results are further explained using confirmatory factor analysis. The proposed method completely removes the challenge of subjectivity associated with dimensionality detection.

DIMENSIONALITY DETECTION, KMO, SIMILARITY DETECTOR, THRESHOLD SETTING