Keywords: The major challenge of data perturbation is to achieve the desired balance between the level of privacy guarantee and the level of data utility. Data privacy and data utility are commonly considered as a pair of conflicting requirements in privacy-preserving data mining systems and applications. Multiplicative perturbation algorithms aim at improving data privacy while maintaining the desired level of data utility by selectively preserving the mining task and model specific information during the data perturbation process. By preserving the task and model specific information, a set of “transformation-invariant data mining models ” can be applied to the perturbed data directly, achieving the required model accuracy. Often a multiplicative perturbation algorithm may find multiple data transformations that preserve the required data utility. Thus the next major challenge is to find a good transformation that provides a satisfactory level of privacy guarantee. In this chapter, we review three representative multiplicative perturbation methods: rotation perturbation, projection perturbation, and geometric perturbation, and discuss the technical issues and research challenges. We first describe the mining task and model specific information for a class of data mining models, and the transformations that can (approximately) preserve the information. Then we discuss the design of appropriate privacy evaluation models for multiplicative perturbations, and give an overview of how we use the privacy evaluation model to measure the level of privacy guarantee in the context of different types of attacks.