Measures of Scatter and Fisher Discriminant Analysis for Uncertain Data

Abstract

Uncertain data objects are objects that can be characterized by either a probability density function (PDF) or with multiple points. Because of existing levels of uncertainty for uncertain data objects, the scatter of this type of objects might be very different than the scatter of certain data objects. Measures of scatter for uncertain objects have not been defined before. In this paper, we define covariance matrix, within scatter matrix, and between scatter matrix as the measures of scatter for uncertain data objects. Also, in this paper, we extend the idea of Fisher linear discriminant analysis for uncertain objects (UFLDA). We also develop kernel Fisher discriminant analysis for uncertain objects (UKFDA). The developed uncertain kernel Fisher discriminants are for two cases: 1) when the uncertain objects are given with PDF and 2) when the uncertain objects are given with multiple points. We compare the performance of our developed uncertain Fisher discriminants (UFLDA and UKFDA) with a few other methods in classification of uncertain data objects through several examples on both simulated and real-world data. We will show in the experiments that our developed uncertain Fisher discriminants outperform other methods in classifying uncertain data objects.