Answering spatial density queries under local differential privacy

Spatial density queries are fundamental in many geospatial data analysis tasks and have numerous applications in the real world, such as determining crowded areas, estimating traffic density, navigation, passenger demand analysis, and so forth. However, answering spatial density queries based on users' data may violate users' privacy by exposing their true locations to an untrusted third party (e.g., a server acting as the service provider or data collector). In this thesis, we propose a solution for answering spatial density queries while preserving Local Differential Privacy (LDP), a state-of-the-art privacy protection standard. Our solution consists of four main steps: partitioning, finding sensitivity, user-side noisy response computation, and server-side estimation. For the first step, we initially propose three basic partitioning strategies: Singleton Partitioning, Holistic Partitioning and Random Partitioning. Based on our qualitative and empirical analysis of the three basic strategies, we design and implement an improved strategy called Advanced Partitioning. For the second step, we adapt graph-based modeling of query sets from the centralized DP literature. Advanced Partitioning also leverages and extends this technique by formulating the partitioning problem as a vertex coloring problem on the graph representation of a query set. For the third and fourth steps, in addition to adapting two popular LDP protocols (GRR and RAPPOR) to our solution, we propose an extension for the Optimized Unary Encoding (OUE) protocol so that it can be employed in our solution. We call the extended protocol Optimized Bitvector Encoding (OBE). OBE is applicable to not only the problem of answering spatial density queries, but also in arbitrary LDP problems with bitvector encodings. We formally prove that the user-side perturbation step of our OBE protocol satisfies LDP and its server-side estimation step produces unbiased estimates. Combining the different partitioning strategies and LDP protocols, we obtain a total of 8 different approaches for answering spatial density queries under LDP, all of which can be parsed as instances of our four-step solution with different choices in the individual steps. We perform an extensive experimental evaluation of these approaches using 4 real-world datasets, varying number of queries, varying query sizes, varying degrees of privacy, and multiple error metrics. Results show that Advanced Partitioning and OBE protocol typically yield the lowest error, demonstrating the superiority of our proposed methods.