Data exchange and data publishing is an inherent component of our interconnected world. Industrial companies outsource datasets to marketing and mining firms in order to support business intelligence; medical institutions exchange collected clinical experiments; academic institutions create repositories and share datasets for promoting research collaboration. A common denominator in any data exchange is the 'transformation' of the original data, which usually results in 'distortion' of data. While accurate and useful information can be potentially distilled from the original data, operations such as anonymization, rights protection and compression result in modified datasets that very seldom retain the mining capacity of its original source. This proposal seeks to address questions such as the following:- How can we lossy compress datasets and still guarantee that mining operations are not distorted?- Is it possible to right protect datasets and provide assurances that this task shall not impair our ability to distill useful knowledge?- To what extent can we resolve data anonymization issues and yet retain the mining capacity of the original dataset?We will examine a fundamental and hard problem in the area of knowledge discovery, which is the delicate balance between data transformation and data utility under mining operations. The problem lies at the confluence of many areas, such as machine and statistical learning, information theory, data representation and optimization. We will focus on studying data transformation methods (compression, anonymization, right protection) that guarantee the preservation of the salient dataset characteristics, such that data mining operations on original and transformed dataset are retained as well as possible. We will investigate how graph-centric approaches, clustering, classification and visualization algorithms can be ported to work under the proposed mining-preservation paradigm. Additional research challenges i