  The characteristics (or numerical patterns) of a feature vector in the
transform domain of a perturbation model differ significantly from those of its
corresponding feature vector in the input domain. These differences - caused by
the perturbation techniques used for the transformation of feature patterns -
degrade the performance of machine learning techniques in the transform domain.
In this paper, we proposed a nonlinear parametric perturbation model that
transforms the input feature patterns to a set of elliptical patterns, and
studied the performance degradation issues associated with random forest
classification technique using both the input and transform domain features.
Compared with the linear transformation such as Principal Component Analysis
(PCA), the proposed method requires less statistical assumptions and is highly
suitable for the applications such as data privacy and security due to the
difficulty of inverting the elliptical patterns from the transform domain to
the input domain. In addition, we adopted a flexible block-wise dimensionality
reduction step in the proposed method to accommodate the possible
high-dimensional data in modern applications. We evaluated the empirical
performance of the proposed method on a network intrusion data set and a
biological data set, and compared the results with PCA in terms of
classification performance and data privacy protection (measured by the blind
source separation attack and signal interference ratio). Both results confirmed
the superior performance of the proposed elliptical transformation.
