| Summary: | 碩士 === 國立東華大學 === 應用數學系 === 98 === Facial attractivness has been a continual interest for researchers and laymen alike. Galton (1883) suggests that not only the beauty lies in the averageness but averageness is beauty. Strauss (1979) suggests also people, even infants, feel certain kindredness to the average faces even that they have never seen these faces before. Although Langlois and Roggman (1990) and Perrett et al. (1994) provide strong evidence that averageness does not equivalent to attractiveness, modification and some further articulation are needed. Nonetheless, the averageness theory provides a unifying and powerful framework for understanding human facial attractiveness. The average theory is fundamentally a uni-prototype theory. Recently, Chang and Chou (2009) proposes an innovative bi-prototypical view of facial attractiveness.Upon this new framework, classification methods have been proposed and result in impressive classification accuracy between attractive and unattractive faces. We think the bi-prototype theory for attractiveness is insightful, however, the classification methods for implemention can be improved. Binary/multiclass classifiers abound in the literature of machine learning. They can be readily tranformed for bi-prototype/multi-prototype classification problems. In this study, we take Fisher Discriminant Analysis (FDA) as a starting point. In the context of facial attractiveness study, the categorical explanatory variables are typicall present. Besides, suitable variable selection is needed. We study these two issues of FDA using some benchmark data sets and simulation data. Our empirical evidence suggests that variable selection and suitable coding of categorical explanatory variables improve the classification accuracy.
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