We examine Euclidean distance-preserving data perturbation as a tool for privacy-preserving data mining. Such perturbations allow many important data mining algorithms e.g. hierarchical and k-means clustering), with only minor modification, to be applied to the perturbed data and produce exactly the same results as if applied to the original data. However, the issue of how well the privacy of the original data is preserved needs careful study. We engage in this study by assuming the role of an attacker armed with a small set of known original data tuples (inputs). Little work has been done examining this kind of attack when the number of known original tuples is less than the number of data dimensions. We focus on this important case, develop and rigorously analyze an attack that utilizes any number of known original tuples. The approach allows the attacker to estimate the original data tuple associated with each perturbed tuple and calculate the probability that the estimation results in a privacy breach. On a real 16-dimensional dataset, we show that the attacker, with 4 known original tuples, can estimate an original unknown tuple with less than 7 error with probability exceeding 0.8.
Before we briefly describe another two attacks based on independent component analysis (ICA) @cite_20 , it is necessary to give a brief ICA overview.
@cite_20
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A fundamental problem in neural network research, as well as in many other disciplines, is finding a suitable representation of multivariate data, i.e. random vectors. For reasons of computational and conceptual simplicity, the representation is often sought as a linear transformation of the original data. In other words, each component of the representation is a linear combination of the original variables. Well-known linear transformation methods include principal component analysis, factor analysis, and projection pursuit. Independent component analysis (ICA) is a recently developed method in which the goal is to find a linear representation of non-Gaussian data so that the components are statistically independent, or as independent as possible. Such a representation seems to capture the essential structure of the data in many applications, including feature extraction and signal separation. In this paper, we present the basic theory and applications of ICA, and our recent work on the subject.