SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

Pattern recognition in statistical analysis: an application of Fourier descriptors to identify shapes in survey research in higher education

Rüdiger Mutz
ETH Zürich

In applied psychology profiles are commonly used to illustrate the differences between groups in several measured properties. Profiles can be characterized by three parameters a) elevation, the level of the profile, b) scatter, the deviation of the profile from the elevation and c) the shape of the profile, which can be analysed by certain kinds of discriminant analysis (Mutz, 2004).

Concerning the shape-parameter these statistical methods don't take into account the qualitative nature of a shape. In this paper a solution to this problem will be presented, which has its roots in pattern recognition in Artifical Intelligence (Breiman, 2001): a profile can be recognized as a planar closed shape, which makes it possible to apply Fourier transformation to extract relevant features.

Burkhardt & Siggelkow (2002) suggested a special kind of Fourier transformation to estimate Fourier descriptors, which are independent of size and location. Because of thet, the shape of the profile can be identified and can compared with presumed shapes, for example circle, oval, star.

Fourier transformation provides not only data reduction but also an optimal statistical fit to the raw profile as defined by Least-Squares estimation. This approach will be adopted for statistical analysis of data of a survey of 1490 undergraduate students in 2001. The main objectives are to classify students by identifying their profile shapes in selected batteries of ratingscales and and to compare them with presumed shapes. A self-programmed SAS-Macro will be presented.


Breiman, L. (2001). Statistical Modeling: The two cultures. Statistical Science, 16(3), 199-231.

Burkhardt, H. & Siggelkow, S. (2002). Invariant features in pattern recognition: fundamentals and applications. In C. Kotropoulos, J. Pitas (Eds.), Nonlinear model-based image / video processing and analysis (p.261-297). New York: John Wiley.

Mutz, R. (2004). Profilanalyse in der Lehrevaluationsforschung. Empirische Pädagogik (accepted paper).