Mining performance data through nonlinear PCA with optimal scaling

Performance data are usually collected in order to build well-defined performance indicators. Since such data may conceal additional information, which can be revealed by secondary analysis, we believe that mining of performance data may be fruitful. We also note that performance databases usually contain both qualitative and quantitative variables for which it may be inappropriate to assume some specific (multivariate) underlying distribution. Thus, a suitable technique to deal with these issues should be adopted. In this work, we consider nonlinear principal component analysis (PCA) with optimal scaling, a method developed to incorporate all types of variables, and to discover and handle nonlinear relationships. Optimal scaling is a framework for multivariate data analysis that is based on two main ideas. First, both nominal and ordinal variables can be optimally transformed to variables with numeric properties. Second, optimal nonlinear transformations of the original variables may be used to overcome the linear assumption underlying all the classic multivariate methods. The reader is offered a case study in which a student opinion database is mined. Though generally gathered to provide evidence of teaching ability, they are exploited here to provide a more general performance evaluation tool for those in charge of managing universities. We show how nonlinear PCA with optimal scaling applied to student opinion data enables users to point out some strengths and weaknesses of educational programs and services within a university.