Clustering and analyzing on collected data can improve user experiences and quality of services in big data, IoT applications. However, directly releasing original data brings potential privacy concerns, which raises challenges and opportunities for privacy-preserving clustering. In this paper, we study the problem of non-interactive clustering in distributed setting under the framework of local differential privacy. We first extend the Bit Vector, a novel anonymization mechanism to be functionality-capable and privacy-preserving. Based on the modified encoding mechanism, we propose kCluster algorithm that can be used for clustering in the anonymized space. We show the modified encoding mechanism can be easily implemented in existing clustering algorithms that only rely on distance information, such as DBSCAN. Theoretical analysis and experimental results validate the effectiveness of the proposed schemes.
Literately, RAPPOR @cite_1 was proposed for studying client data under the framework of differential privacy. In one-time RAPPOR, a value @math is first hashed into a bloom filter @math with length @math by a series of hash functions. Then permanent randomized response is added to @math to get @math before reported. However, the one-time RAPPOR mechanism can not be used for distance-aware encoding as the bloom filter is not distance-aware. To facilitate this, we use the BV mechanism as mentioned. Instead of using permanent randomized response, the 1Bit mechanism @cite_7 is used to embed a numerical value. For data from @math to @math , a numerical value is encoded to @math with probability @math .
@cite_1 @cite_7
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Randomized Aggregatable Privacy-Preserving Ordinal Response, or RAPPOR, is a technology for crowdsourcing statistics from end-user client software, anonymously, with strong privacy guarantees. In short, RAPPORs allow the forest of client data to be studied, without permitting the possibility of looking at individual trees. By applying randomized response in a novel manner, RAPPOR provides the mechanisms for such collection as well as for efficient, high-utility analysis of the collected data. In particular, RAPPOR permits statistics to be collected on the population of client-side strings with strong privacy guarantees for each client, and without linkability of their reports. This paper describes and motivates RAPPOR, details its differential-privacy and utility guarantees, discusses its practical deployment and properties in the face of different attack models, and, finally, gives results of its application to both synthetic and real-world data. We study the problem of estimating @math -ary distributions under @math -local differential privacy. @math samples are distributed across users who send privatized versions of their sample to a central server. All previously known sample optimal algorithms require linear (in @math ) communication from each user in the high privacy regime @math , and run in time that grows as @math , which can be prohibitive for large domain size @math . @PARASPLIT We propose Hadamard Response (HR), a local privatization scheme that requires no shared randomness and is symmetric with respect to the users. Our scheme has order optimal sample complexity for all @math , a communication of at most @math bits per user, and nearly linear running time of @math . @PARASPLIT Our encoding and decoding are based on Hadamard matrices and are simple to implement. The statistical performance relies on the coding theoretic aspects of Hadamard matrices, ie, the large Hamming distance between the rows. An efficient implementation of the algorithm using the Fast Walsh-Hadamard transform gives the computational gains. @PARASPLIT We compare our approach with Randomized Response (RR), RAPPOR, and subset-selection mechanisms (SS), both theoretically, and experimentally. For @math , our algorithm runs about 100x faster than SS, and RAPPOR. The performance of a novel fountain coding scheme based on maximum distance separable (MDS) codes constructed over Galois fields of order q>=2 is investigated. Upper and lower bounds on the decoding failure probability under maximum likelihood decoding are developed. Differently from Raptor codes (which are based on a serial concatenation of a high-rate outer block code, and an inner Luby-transform code), the proposed coding scheme can be seen as a parallel concatenation of an outer MDS code and an inner random linear fountain code, both operating on the same Galois field. A performance assessment is performed on the gain provided by MDS based fountain coding over linear random fountain coding in terms of decoding failure probability vs. overhead. It is shown how, for example, the concatenation of a (15,10) Reed-Solomon code and a linear random fountain code over F16 brings to a decoding failure probability 4 orders of magnitude lower than the linear random fountain code for the same overhead in a channel with a packet loss probability of epsilon=0.05. Moreover, it is illustrated how the performance of the concatenated fountain code approaches that of an idealized fountain code for higher-order Galois fields and moderate packet loss probabilities. The scheme introduced is of special interest for the distribution of data using small block sizes. Consider the recovery of an unknown signal @math from quantized linear measurements. In the one-bit compressive sensing setting, one typically assumes that @math is sparse, and that the measurements are of the form @math . Since such measurements give no information on the norm of @math , recovery methods from such measurements typically assume that @math . We show that if one allows more generally for quantized affine measurements of the form @math , and if the vectors @math are random, an appropriate choice of the affine shifts @math allows norm recovery to be easily incorporated into existing methods for one-bit compressive sensing. Additionally, we show that for arbitrary fixed @math in the annulus @math , one may estimate the norm @math up to additive error @math from @math such binary measurements through a single evaluation of the inverse Gaussian error function. Finally, all of our recovery guarantees can be made universal over sparse vectors, in the sense that with high probability, one set of measurements and thresholds can successfully estimate all sparse vectors @math within a Euclidean ball of known radius.