MANOVA, LDA, and FA criteria in clusters parameter estimation

• Main Author: Stan Lipovetsky
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2015-12-01
• Series: Cogent Mathematics
• Subjects: MANOVA; LDA; Wilks’ lambda; Lawley–Hotelling trace; Pillai’s trace; Joreskog’s classification for FA; cluster analysis; multinomial optimization
• Online Access: http://dx.doi.org/10.1080/23311835.2015.1071013

Multivariate analysis of variance (MANOVA) and linear discriminant analysis (LDA) apply such well-known criteria as the Wilks’ lambda, Lawley–Hotelling trace, and Pillai’s trace test for checking quality of the solutions. The current paper suggests using these criteria for building objectives for finding clusters parameters because optimizing such objectives corresponds to the best distinguishing between the clusters. Relation to Joreskog’s classification for factor analysis (FA) techniques is also considered. The problem can be reduced to the multinomial parameterization, and solution can be found in a nonlinear optimization procedure which yields the estimates for the cluster centers and sizes. This approach for clustering works with data compressed into covariance matrix so can be especially useful for big data.