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Grid-Based Decompositions for Spatial Data under Local Differential Privacy

Berkay Kemal Balioglu, Alireza Khodaie, Ameer Taweel, Mehmet Emre Gursoy

TL;DR

The paper tackles private release of spatial statistics under Local Differential Privacy by evaluating grid-based decompositions. It introduces Advanced Adaptive Grid (AAG), a neighbor-aware, uneven cell-division method, and systematically compares it with Uniform Grid (UG) and PrivAG across three real-world datasets, varying $\varepsilon$ and query size. Empirical results show AAG consistently improves over PrivAG and often outperforms UG for small, detailed queries, though UG may dominate for large, coarse queries with near-optimal grid sizing. The work advances practical LDP spatial analytics by highlighting the benefits of neighbor-informed adaptivity and providing guidance on when to prefer adaptive grids versus static grids in different query regimes.

Abstract

Local differential privacy (LDP) has recently emerged as a popular privacy standard. With the growing popularity of LDP, several recent works have applied LDP to spatial data, and grid-based decompositions have been a common building block in the collection and analysis of spatial data under DP and LDP. In this paper, we study three grid-based decomposition methods for spatial data under LDP: Uniform Grid (UG), PrivAG, and AAG. UG is a static approach that consists of equal-sized cells. To enable data-dependent decomposition, PrivAG was proposed by Yang et al. as the most recent adaptive grid method. To advance the state-of-the-art in adaptive grids, in this paper we propose the Advanced Adaptive Grid (AAG) method. For each grid cell, following the intuition that the cell's intra-cell density distribution will be affected by its neighbors, AAG performs uneven cell divisions depending on the neighboring cells' densities. We experimentally compare UG, PrivAG, and AAG using three real-world location datasets, varying privacy budgets, and query sizes. Results show that AAG provides higher utility than PrivAG, demonstrating the superiority of our proposed approach. Furthermore, UG's performance is heavily dependent on the choice of grid size. When the grid size is chosen optimally in UG, AAG still beats UG for small queries, but UG beats AAG for large (coarse-grained) queries.

Grid-Based Decompositions for Spatial Data under Local Differential Privacy

TL;DR

The paper tackles private release of spatial statistics under Local Differential Privacy by evaluating grid-based decompositions. It introduces Advanced Adaptive Grid (AAG), a neighbor-aware, uneven cell-division method, and systematically compares it with Uniform Grid (UG) and PrivAG across three real-world datasets, varying and query size. Empirical results show AAG consistently improves over PrivAG and often outperforms UG for small, detailed queries, though UG may dominate for large, coarse queries with near-optimal grid sizing. The work advances practical LDP spatial analytics by highlighting the benefits of neighbor-informed adaptivity and providing guidance on when to prefer adaptive grids versus static grids in different query regimes.

Abstract

Local differential privacy (LDP) has recently emerged as a popular privacy standard. With the growing popularity of LDP, several recent works have applied LDP to spatial data, and grid-based decompositions have been a common building block in the collection and analysis of spatial data under DP and LDP. In this paper, we study three grid-based decomposition methods for spatial data under LDP: Uniform Grid (UG), PrivAG, and AAG. UG is a static approach that consists of equal-sized cells. To enable data-dependent decomposition, PrivAG was proposed by Yang et al. as the most recent adaptive grid method. To advance the state-of-the-art in adaptive grids, in this paper we propose the Advanced Adaptive Grid (AAG) method. For each grid cell, following the intuition that the cell's intra-cell density distribution will be affected by its neighbors, AAG performs uneven cell divisions depending on the neighboring cells' densities. We experimentally compare UG, PrivAG, and AAG using three real-world location datasets, varying privacy budgets, and query sizes. Results show that AAG provides higher utility than PrivAG, demonstrating the superiority of our proposed approach. Furthermore, UG's performance is heavily dependent on the choice of grid size. When the grid size is chosen optimally in UG, AAG still beats UG for small queries, but UG beats AAG for large (coarse-grained) queries.
Paper Structure (17 sections, 8 equations, 2 figures, 5 tables, 3 algorithms)

This paper contains 17 sections, 8 equations, 2 figures, 5 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Data Model and Notations
  4. Local Differential Privacy
  5. Optimized Local Hashing
  6. Grid-Based Decompositions Under LDP
  7. Uniform Grid (UG)
  8. Existing Adaptive Grid: PrivAG
  9. Proposed Approach: Advanced Adaptive Grid (AAG)
  10. Experiments and Discussion
  11. Experiment Setup and Datasets
  12. Utility Metric
  13. Uniform Grid Experiments
  14. Comparison of Grid Approaches
  15. Impact of the Privacy Budget $\varepsilon$
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Difference between PrivAG and AAG
  • Figure 2: AQEs of $N \times N$ uniform grids $\mathcal{G}_{uni}$ with varying $N$, fixed $\varepsilon$ = 1. From left to right: Gowalla dataset, Porto dataset, Foursquare dataset.

Theorems & Definitions (1)

  • definition thmcounterdefinition: $\varepsilon$-LDP