Data Mining - Concepts and Techniques.

Data Mining Practical Machine Learning Tools and Techniques

Sphere Packings, Lattices and Groups

Consider a discrete source producing a sequence of message letters from a finite alphabet. A single-letter distortion measure is given by a non-negative matrix (d ij ). The entryd ij measures the ?cost? or ?distortion? if letteriis reproduced at the receiver as letterj. The average distortion of a communications system (source-coder-noisy channel-decoder) is taken to bed= ? i.j P ij d ij whereP ij is the probability ofibeing reproduced asj. It is shown that there is a functionR(d) that measures the ?equivalent rate? of the source for a given level of distortion. For coding purposes where a leveldof distortion can be tolerated, the source acts like one with information rateR(d). Methods are given for calculatingR(d), and various properties discussed. Finally, generalizations to ergodic sources, to continuous sources, and to distortion measures involving blocks of letters are developed. In this paper a study is made of the problem of coding a discrete source of information, given afidelity criterionor ameasure of the distortionof the final recovered message at the receiving point relative to the actual transmitted message. In a particular case there might be a certain tolerable level of distortion as determined by this measure. It is desired to so encode the information that the maximum possible signaling rate is obtained without exceeding the tolerable distortion level. This work is an expansion and detailed elaboration of ideas presented earlier [1], with particular reference to the discrete case. We shall show that for a wide class of distortion measures and discrete sources of information there exists a functionR(d) (depending on the particular distortion measure and source) which measures, in a sense, the equivalent rateRof the source (in bits per letter produced) whendis the allowed distortion level. Methods will be given for evaluatingR(d) explicitly in certain simple cases and for evaluatingR(d) by a limiting process in more complex cases. The basic results are roughly that it is impossible to signal at a rate faster thanC/R(d) (source letters per second) over a memoryless channel of capacityC(bits per second) with a distortion measure less than or equal tod. On the other hand, by sufficiently long block codes it is possible to approach as closely as desired the rateC/R(d) with distortion leveld. Finally, some particular examples, using error probability per letter of message and other simple distortion measures, are worked out in detail.

Coding Theorems for a Discrete Source With a Fidelity CriterionInstitute of Radio Engineers, International Convention Record, vol. 7, 1959.

Elements of Information Theory (2nd ed.). Thomas M. Cover and Joy A. Thomas

t-Closeness is a privacy model recently defined for data anonymization. A data set is said to satisfy t-closeness if, for each group of records sharing a combination of key attributes, the distance between the distribution of a confidential attribute in the group and the distribution of the attribute in the entire data set is no more than a threshold t. Here, we define a privacy measure in terms of information theory, similar to t-closeness. Then, we use the tools of that theory to show that our privacy measure can be achieved by the postrandomization method (PRAM) for masking in the discrete case, and by a form of noise addition in the general case.

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From t-Closeness-Like Privacy to Postrandomization via Information Theory

We present a mathematical formulation for the optimization of query forgery for private information retrieval, in the sense that the privacy risk is minimized for a given traffic and processing overhead. The privacy risk is measured as an information-theoretic divergence between the user's query distribution and the population's, which includes the entropy of the user's distribution as a special case. We carefully justify and interpret our privacy criterion from diverse perspectives. Our formulation poses a mathematically tractable problem that bears substantial resemblance with rate-distortion theory.

/pdf/optimized-query-forgery-for-private-information-retrieval-ru4j0qjsjf.pdf

Optimized Query Forgery for Private Information Retrieval

Measuring the privacy of user profiles in personalized information systems

Recommendation systems and content filtering approaches based on annotations and ratings, essentially rely on users expressing their preferences and interests through their actions, in order to provide personalised content. This activity, in which users engage collectively, has been named social tagging. Although it has opened a myriad of new possibilities for application interoperability on the semantic web, it is also posing new privacy threats. Social tagging consists in describing online or online resources by using free-text labels (i.e. tags), therefore exposing the user's profile and activity to privacy attacks. Tag forgery is a privacy enhancing technology consisting of generating tags for categories or resources that do not reflect the user's actual preferences. By modifying their profile, tag forgery may have a negative impact on the quality of the recommendation system, thus protecting user privacy to a certain extent but at the expenses of utility loss. The impact of tag forgery on content-based recommendation is, therefore, investigated in a real-world application scenario where different forgery strategies are evaluated, and the consequent loss in utility is measured and compared.

Jordi Forné

Papers

From t-Closeness-Like Privacy to Postrandomization via Information Theory

Optimized Query Forgery for Private Information Retrieval

Measuring the privacy of user profiles in personalized information systems

On Content-Based Recommendation and User Privacy in Social-Tagging Systems

On content-based recommendation and user privacy in social-tagging systems