There are a number of studies which identify a set of features and then search for clusters / 'categories' with various methods.

https://en.wikipedia.org/wiki/Linear_discriminant_analysis

> LDA is also closely related to principal component analysis (PCA) and factor analysis in that they both look for linear combinations of variables which best explain the data.[4] LDA explicitly attempts to model the difference between the classes of data. PCA on the other hand does not take into account any difference in class, and factor analysis builds the feature combinations based on differences rather than similarities. Discriminant analysis is also different from factor analysis in that it is not an interdependence technique: a distinction between independent variables and dependent variables (also called criterion variables) must be made.

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> Is anybody else interested in designing a categorical personality theory that can be used to fix yourself

How helpful is personality theory in developing a clinical model for behavior change?