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Yun-Jhong Wu

2011-06-10
12:50:00 - 13:50:00

307 , Mathematics Research Center Building (ori. New Math. Bldg.)

Over the past few decades, within the various fields of science, a gradual but noticeable shift in the focus from binary to multi-classification has taken place. This trend demands a better understand of discriminating capacity of classification procedures. Although a few works have provided illuminating insight about this issue, such as some implementation and extension of receiver operating characteristic (ROC) analysis, a rigorous theoretical groundwork is scant in the extant literature. Our study attempted to build up summary measure for performance of multi-classification markers based on the overall performance of classifiers and naturally introduced a perspective of geometry. It involves a construction of manifolds composing of performance probabilities of classification and investigations of the local structure of the manifolds. The enclosedness of the manifolds provides a reasonable summary assessment of markers in a proper ROC subspaces. The corresponding estimation and inference procedures were developed for a more complete theory of multi-classification, and the numerical studies were devoted to illustrate its practicality.