A cluster-based factor rotation


Correspondence should be addressed to Michio Yamamoto, Division of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan (e-mail: myamamoto@sigmath.es.osaka-u.ac.jp).


A new oblique factor rotation method is proposed, the aim of which is to identify a simple and well-clustered structure in a factor loading matrix. A criterion consisting of the complexity of a factor loading matrix and a between-cluster dissimilarity is optimized using the gradient projection algorithm and the k-means algorithm. It is shown that if there is an oblique rotation of an initial loading matrix that has a perfect simple structure, then the proposed method with Kaiser's normalization will produce the perfect simple structure. Although many rotation methods can also recover a perfect simple structure, they perform poorly when a perfect simple structure is not possible. In this case, the new method tends to perform better because it clusters the loadings without requiring the clusters to be perfect. Artificial and real data analyses demonstrate that the proposed method can give a simple structure, which the other methods cannot produce, and provides a more interpretable result than those of widely known rotation techniques.