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The characteristics (or numerical patterns) of a feature vector in thetransform domain of a perturbation model differ significantly from those of itscorresponding feature vector in the input domain. These differences - caused bythe 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 thattransforms the input feature patterns to a set of elliptical patterns, andstudied the performance degradation issues associated with random forestclassification 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 highlysuitable for the applications such as data privacy and security due to thedifficulty of inverting the elliptical patterns from the transform domain tothe input domain. In addition, we adopted a flexible block-wise dimensionalityreduction step in the proposed method to accommodate the possiblehigh-dimensional data in modern applications. We evaluated the empiricalperformance of the proposed method on a network intrusion data set and abiological data set, and compared the results with PCA in terms ofclassification performance and data privacy protection (measured by the blindsource separation attack and signal interference ratio). Both results confirmedthe superior performance of the proposed elliptical transformation.

Elliptical modeling and pattern analysis for perturbation models and classfication